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MODERN 

TECHNICAL  DRAWINC 


EORGE   ELLIS 


B    3    1D1    511 


MODERN 
TECHNICAL  DRAWING 


( 


MODERN 
TECHNICAL  DRAWING 

A  HANDBOOK  DESCRIBING  IN  DETAIL  THE 
PREPARATION  OF  WORKING  DRAWINGS, 
WITH  SPECIAL  ATTENTION  TO  OBLIQUE 
AND  CIRCLE-ON-CIRCLE  WORK,  ORTHO- 
GRAPHIC, ISOMETRIC  AND  OBLIQUE 
PROJECTIONS,  PRACTICAL  PERSPECTIVE, 
FREEHAND  DRAWING  AND  "SETTING-OUT"; 
ALSO  VARIOUS  STYLES  OF  LETTERING 


GEORGEl  ELLIS-       \£i 

Author  of  "  Modern  Practical  Joinery,"  "  Modern  Ch 

Practical  Carpentry,"  etc.  ' 


\ 


ILLUSTRATED  BY  NEARLY  300  EXAMPLES 


LONDON 
B.   T.    BATSFORD,  94  HIGH   HOLBORN 


CLASS 
PB 


r    T 


T35-3 

E55; 


PREFACE 


\)JLAA*S^ 


THE  object  of  this  little  work  is  to  meet  a  frequently  expressed 
need  for  some  practical  instruction  in  Builders'  Technical 
Drawing  as  pursued  in  the  modern  Office  and  Workshop, 
to  bring  together  in  due  order  the  various  methods  and 
devices  obtaining  in  the  preparation  of  Working  Drawings, 
and  to  explain  their  principles  and  indicate  the  suitability  or 
otherwise,  for  the  purpose  in  view. 

Although  no  attempt  has  been  made  to  treat  the  subject 
exhaustively,  sufficient  information,  it  is  hoped,  has  been  given 
to  enable  the  beginner  to  reach  a  considerable  degree  of  pro- 
ficiency without  further  aid  than  the  numerous  examples 
provided  will  afford.  It  is  also  believed  that  Teachers  of 
Drawing  may  find  in  these  examples  some  useful  suggestions 
for  their  own  demonstrations. 

For  the  sake  of  completeness,  a  form  of  Technical  Drawing 
not  usually  associated  with  draughtmen's  work,  but  none  the 
less  important — viz.  the  planning  and  graphic  description  of 
work  for  the  use  of  artisans  in  the  workshop  known  collectively 
as  the  "  Setting-Out "  of  work — is  included  and  treated  with  a 
fulness  not  hitherto  attempted,  and  this,  it  is  hoped,  will  prove 
of  service  to  foremen  and  others. 

I  take  this  opportunity  of  acknowledging  the  assistance  of 
Miss  Gertrude  Ellis  and  Mr  George  Ellis,  jun.,  in  arranging 
and  preparing  the  book  for  the  press.::  .. 

THE  AUTHOR 

ILFORD, 
September  1913. 


001-15 


CONTENTS 


CHAPTER  PAGE 

I.  TECHNICAL  DRAWING     .  .  .  .  i 

Description  and  Comparison  of  the  Various  Kinds  of 
Drawings  used  by  Technical  Draughtsmen,  their  Advan- 
tages and  Limitations 

II.  DRAWING  INSTRUMENTS  . '  .  .8 

Materials,  Appliances  and  Accessories — how  to  use  them 

III.  DRAUGHTSMAN'S  WORK  .  ,  ,        24 

With  Hints  on  Drawing  and  Inking,  Standard  List  of 
Sectionings,  Lines  and  Signs,  etc. 

IV.  LETTERING  DRAWINGS  .  .  .  -35 

Chief  Modern  Types  of  Letters  and  Numerals, 
Uniformity,  Spacing,  Balance,  Proportion,  Optical 
Corrections,  Alphabets,  Tools 

V.  ORTHOGRAPHIC  PROJECTION      .  ."  .46 

Plans,  Elevations,  Sections  with  examples  in  Carpentry, 
Cabinetwork,  Joinery,  Brickwork  and  Masonry,  including 
Cupboards,  Counters,  Doors,  Gates,  Roofs,  Floors, 
Windows,  Lanterns,  Circle-on-Circle  Work 

VI.  ISOMETRIC  PROJECTION  .  .  .  .82 

Theory  of  Parish's  Method.  The  modern  Methods. 
Preparing  Scales.  Examples  in  Shop  Fittings.  Brick- 
work. Builder's  Gantry.  Pyramids,  Cylinders  and 
Curves 

VII.  OBLIQUE  PROJECTION     ....       100 

Its  Uses,  Scales,  Official  Method.  Half-Scale  Work. 
A  new  Method  by  the  Author.  Examples  in  Partitioning, 
Reinforced  Concrete  Forms,  Ship's  Grating,  etc. 

vii 


viii  CONTENTS 

CHAPTER  PAGE 

VIII.  PRACTICAL   PERSPECTIVE  .  .  .114 

As  used  by  Architectural  Draughtsmen.  Principles. 
Methods  of  producing  Drawings  without  Vanishing 
Points.  Examples  in  Masonry,  Carpentry  and  Cabinet 
Work 

IX.  FREEHAND  DRAWING     ,  .  .  .127 

and  Sketching  for  Artisans.  I  low  to  draw  Curved  Lines. 
Use  of  Squared  Paper.  Enlarging  and  Diminishing 
Drawings.  Tracing  Paper,  use  of.  Examples  in 
Joinery,  Masonry,  Hinges,  Door  Springs,  etc. 

X.  PRACTICAL  GEOMETRY   .  .  .  .       141 

Obtaining  Bevels  and  Cuts  in  Simple  and  Compound 
Angles.  Development  of  Surfaces,  Moulds  for  Double 
Curved  Work.  Forming  Complex  Curves,  Helix, 
Spiral,  Scroll,  etc.  The  Conic  Sections,  Drawing 
Ellipses,  Covering  of  Domes,  Setting-out  Arches  in 
Brickwork,  Masonry  and  Carpentry.  A  Handrail  Wreath 

XI.  WORKSHOP  DRAWINGS    .  '.  ...  .       178 

Methods  in  different  Trades.  The  Setting-out  of 
JOINERS'  RODS.  What  to  put  on  a  Rod,  what  to 
omit.  A  Venetian  Frame.  A  Pair  of  Circular-headed 
Doors  and  Finishings.  BRICKLAYERS'  SETTING-OUT. 
Circle-on-Circle  Work.  Obtaining  Moulds.  Octagonal 
Chimney  Stack.  Setting-out  Octagons  Bevels  for 
Templets 

INDEX  .       194 


Modern  Technical  Drawing 

CHAPTER   I 
VARIOUS  KINDS   OF  TECHNICAL  DRAWING 

Technical  Drawings — the  requirements  of,  need  of  conventions. 
Orthographic  Projection — principles  of.  Isometric  Projection 
— its  uses  and  defects.  Oblique  Projection — various  modi- 
fications. Perspective  Projection  —  what  it  is.  Freehand 
Sketches — advantages  of.  Practical  Geometry — its  use  to  the 
draughtsman.  Working  Drawings — essentials  of.  Workshop 
Drawing 

Technical  Drawing  is,  in  effect,  the  language  of  the 
workshop  and  drawing  office,  the  means  by  which  the  ideas 
or  intentions  of  the  designer  are  conveyed  to  the  constructor 
in  a  much  more  definite  and  understandable  manner  than 
can  be  done  by  the  most  elaborately  written  or  spoken 
directions. 

It  will  be  readily  understood  that,  to  avoid  confusion, 
universally  accepted  methods  or  conventions  must  be 
adhered  to  in  preparing  such  drawings,  otherwise  the  user 
would  be  in  the  same  position  as  one  trying  to  read  a  book 
written  in  a  foreign  language  ;  even  the  latitude  allowed 
the  artist  or  pictorial  draughtsman  in  depicting  his  emotions 
or  impressions  would  render  technical  drawings  useless  for 
their  purpose.  We  must  speak  in  a  common  language  to 
be  understood  by  all. 

But  the  requirements  of  the  constructive  arts  are  so 
numerous  and  varied  that  even  within  the  circumscribed 
sphere  of  the  building  trades  several  different  types  or 
classes  of  drawing  are  necessary.  Each  of  these  will  be 
dealt  with  as  fully  as  may  be  needful  for  elementary  work 


2  ORTHOGRAPHIC    PROJECTION 

in  the  succeeding  chapters,  and  the  descriptions  given  here 
are  rather  in  the  nature  of  a  summary  of  the  advantages 
and  disadvantages — or  at  least  the  limitations  of  each 
kind — than  an  instruction  in  their  preparation. 

Orthographic  or  Perpendicular  Projection. — This 
is  the  commonest  and  most  useful  method  of  producing 
drawings,  but  its  meaning  is  not  always  obvious  to  the 
inexperienced,  for  it  is  a  graphic  language  that  generally 
has  to  be  acquired  step  by  step.  In  this  form  of  drawing, 
which  is  usually  adopted  for  architectural  "  plans  "  of 
buildings  and  for  working  drawings,  every  part  is  drawn 
as  if  immediately  in  front  of  the  observer,  no  allowance 
for  distance  in  the  parts  of  the  object  from  the  observer 
being  made  ;  it  is  the  unaccustomed  appearance  which 
results  when  this  method  is  used  that  is  so  confusing  to 
the  uninitiated,  but  the  procedure  is  essential  if  direct 
measurements  and  correct  angles  are  to  be  obtained  from 
the  drawings.  In  this  kind  of  drawing  the  observer  is 
supposed  to  stand  directly  in  front  of  the  object,  and  to 
see  all  its  parts  upon  that  face  at  the  same  time,  and  it 
will  be  obvious  that,  if  this  is  so,  he  cannot  see  more  than 
one  front  or  surface  at  a  time ;  consequently,  in  depicting 
any  solid,  as  many  "  projections  "  or  views  have  to  be 
made  as  the  solid  has  sides  or  surfaces.  As,  often,  the 
several  sides  do  not  possess  distinctive  features  by  which 
they  can  be  readily  identified,  a  conventional  or  generally- 
agreed-upon  set  of  terms  are  used  to  describe  these  views, 
mainly  based  upon  their  relative  position  to  the  ground. 
Thus  the  surface  or  side  which  is  supposed  to  rest  upon, 
or  is  parallel  to,  the  surface  of  the  ground  is  termed  the 
PLAN  ;  that  surface  which  is  at  right  angles  to  the  ground — - 
i.e.  vertical — is  termed  the  ELEVATION,  and  as  there  are 
only  three  dimensions  to  any  solid — viz.  length,  breadth 
and  thickness — it  is  obvious  that  we  can  depict  any  regular 
solid  by  three  views  or  projections  showing  these  dimensions. 
One  of  these  will  be  the  PLAN,  the  other  two  will  be  ELEVA- 
TIONS, which  are  distinguished  as  circumstances  dictate, 


ISOMETRIC    PROJECTION  3 

either  as  the  "  front  elevation  "  and  "  end  elevation,"  or, 
as  in  the  case  of  buildings,  according  to  the  point  of  the  com- 
pass which  they  face,  as  north,  south,  east  or  west,  etc., 
elevations.  If  the  object  depicted  has  an  interior  which  it 
is  desired  to  show,  such  a  view  is  termed  a  SECTION,  which 
means  a  cutting,  the  view  produced  being  that  which  the 
observer  would  see  if  the  object  were  cut  through  on, 
or  by,  a  plane  parallel  to  that  upon  which  the  drawing 
is  made. 

As  the  object  here  is  merely  to  summarise  the  character- 
istics of  the  various  kinds  of  drawing,  further  details  will 
be  deferred  until  the  chapter  dealing  with  the  method  of 
making  orthographic  projections  is  reached.  The  drawings 
upon  page  4  illustrate,  by  means  of  a  simple  solid,  the  several 
methods  herein  described,  from  which  a  ready  comparison 
of  their  effect  can  be  drawn. 

Isometric  Projection  or  Projection  of  Equal 
Measures  is  a  method  used  to  depict  three  sides  of  an 
object  in  one  drawing,  thus  showing  its  length,  breadth 
and  thickness  with  a  minimum  of  work  and  a  maximum 
of  clearness ;  it  is  a  suitable  and  convincing  method  for 
rectangular  objects  only,  as  those  with  inclined  surfaces  are 
so  distorted  in  the  drawing  that  no  true  impression  of  their 
shape  is  conveyed  by  this  method. 

Its  limitations  will  be  dealt  with  more  fully  in  Chapter 
VI.  Here  it  will  be  sufficient  to  draw  attention  to  the  in- 
clined mitre  in  the  "  frog  "  of  the  brick  depicted  in  Fig.  6, 
page  4,  wherein  the  junction  between  the  two  slopes  is 
indicated  by  a  vertical  line,  which  common-sense  tells  us  it 
is  not.  However,  it  is  impossible  to  show  it  in  any  other 
way  by  the  rules  of  isometric  projection. 

Oblique  or  Parallel  Projection  is  a  still  simpler  method 
than  the  last  for  showing  three  sides  of  an  object  in  one 
drawing.  Simple  rectangular  solids,  or  those  having 
regular  curved  outlines  such  as  mouldings,  can  be  shown  in 
this  way  easily  and  graphically  (see  Fig.  7,  page  6).  In 
this  method  the  chief  face,  or  elevation,  is  drawn  as  it  exists 


PERSPECTIVE    PROJECTION  5 

or  is  intended,  and  the  two  adjacent  sides  are  then  drawn 
at  a  common  oblique  angle,  most  frequently  45°,  all  of  the 
sides  which  are  parallel  in  the  object  being  drawn  parallel 
in  the  projection.  The  chief  drawback  of  this  method  is 
that  the  oblique  sides  appear  out  of  proportion  to  the 
adjacent  side. 

Two  modifications  of  the  method  have  been  adopted  to 
counteract  this  effect :  one  by  drawing  the  oblique  side  to 
half  the  scale  of  the  parallel  side  ;  the  other  by  making  an 
auxiliary  drawing  from  which  the  projection  is  made  upon  a 
special  picture  plane. 

The  first  method  sins  against  a  cardinal  rule  of  draughts- 
manship, in  using  two  scales  or  proportions  upon  one  object, 
a  fruitful  source  of  error.  The  second  is  a  complicated  and 
involved  process,  with  little  to  recommend  it  upon  the  score 
of  economy  of  time.  The  three  methods  are  explained  in 
detail  in  Chapter  VII.,  together  with  another  method  used 
by  the  author  for  some  years,  but  now  published  for  the 
first  time. 

Perspective  or  Radial  Projection  represents  solids  by 
means  of  diagrams  in  which  each  geometrical  "  point  "  is 
defined  upon  the  plane  of  the  drawing  by  a  projector,  which 
passes  through  the  actual  point  represented  and  through  a 
fixed  point  which  is  the  same  for  all  the  points  in  the  draw- 
ing. The  position  of  this  fixed  point  in  relation  to  the  plane 
of  the  drawing  and  to  the  object  represented  must  be 
selected  within  certain  limits,  or  an  appearance  of  distortion 
will  result  in  the  drawing. 

This  method  of  drawing  shows  objects  in  the  positions 
in  which  they  appear  to  be  in  relation  to  the  eye  of  the 
observer,  and  not  as  they  really  exist.  Thus  a  long,  straight 
track  of  railway  lines  is  made  to  appear  as  though  converging 
in  the  distance,  though  of  course  they  are  in  fact^parallel, 
but  by  representing  them  in  this  manner  we  produce  the 
impression  of  distance  for  the  observer. 

It  is  not  necessary  in  this  small  treatise  to  explain  fully 
the  theory  of  linear  perspective,  for  it  is  only  intended  to 


6  FREEHAND    DRAWING 

give  the  abbreviated  method  commonly  used  by  technical 
draughtsmen. 

Freehand  Drawing  and  Sketching.— This  term 
implies  drawing  or  sketching  in  which  the  hand  of  the  worker 
is  "  free  "  in  the  sense  of  not  being  guided  or  restricted  in 
its  action  by  any  mechanical  means  such  as  squares,  com- 
passes or  rulers. 

The  result  depends  upon  the  skill  or  practice  of  the 
sketcher.  It  is  an  acquirement  worth  cultivating,  as  often 
a  graphic  sketch  made  in  a  few  seconds  will  illustrate  one's 
meaning  much  more  readily  than  a  laborious  verbal  de- 
scription. In  Chapter  IX.  will  be  found  a  few  hints  and 
devices  that  the  author  has  found  of  assistance  in  his  own 
practice. 

Practical  Geometry. — Geometry  is  denned  as  that 
branch  of  mathematics  which  treats  of  the  measurements  of 
lines,  surfaces  and  solids,  with  their  various  relations  ;  and 
practical  geometry  is  the  method  of  applying  its  principles 
to  the  requirements  of  trades  or  handicraft. 

Almost  all  mechanical  drawing  is  based  on  geometrical 
principles,  and  in  the  chapter  which  is  devoted  to  this 
subject  a  selection  of  examples  is  given  in  which  it  is  shown 
how  these  well-established  principles  may  be  utilised  in 
solving  the  everyday  problems  of  the  workshop  .and 
drawing  office. 

Working  Drawings. — The  term,  working  drawing,  is 
commonly  used  by  architects  to  indicate  those  drawings 
which  they  supply  to  builders  as  part  of  the  necessary 
directions  for  doing  the  work.  These  drawings  vary  in  scale 
from  |  in.  to  the  foot,  or  even  smaller,  up  to  full  size,  accord- 
ing to  convenience  or  necessity.  Further  working  drawings 
are  generally  made  from  these,  for  the  direct  use  of  the 
workman ;  these  are,  in  carpenters'  and  joiners'  work 
particularly,  practically  always  full  size,  and  are  generally 
made  (or  set  out,  as  it  is  termed)  by  the  foreman  or  a  specially 
efficient  workman  termed  a  "  setter-out."  These  full-size 
drawings  are  usually  made  upon  prepared  boards  termed 


RODS  7 

"  rods,"  and  it  is  from  these  that  the  working  lines  are 
transferred  to  the  material,  or,  as  in  the  case  of  brickwork 
and  masonry,  the  working  templets  are  made.  It  might 
perhaps  be  convenient  to  distinguish  these  latter  as  "  work- 
shop "  drawings,  but,  of  course,  the  distinction  would  be  a 
purely  arbitrary  one. 


CHAPTER  II 

DRAWING  INSTRUMENTS  AND  APPLIANCES- 
HOW   TO    USE   THEM 

The  Drawing  Board — sizes,  materials,  attachments,  a  reversible 
board.  Squares  —  T-square,  most  serviceable  kind.  Set 
Squares — useful  sizes,  various  materials  and  their  defects. 
French  Curves.  Instruments — choice  of.  Compasses — sizes, 
uses,  etc.  Ruling  Pen.  Parallels.  Protractors — description, 
various  kinds,  construction  of,  method  of  using.  Drawing 
Papers — choice  of,  where  obtainable,  standard  sizes.  Pencils — 
degrees,  making  compass  pencils.  Rubber — kinds,  and  methods 
of  using.  Drawing  Pins.  Extractors.  Drawing  Inks — how  to 
prepare  and  use.  Tracing  Paper  and  Cloth — sizes  and  use  of. 
Scales — description,  making  scales,  the  representative  fraction, 
method  of  dividing,  diagonal  scales,  how  constructed  and  read 

The  Drawing  Board. — This  is  a  flat  board  with  its 
edges  truly  square  and  parallel,  made  in  certain  standard 
sizes  to  suit  the  paper  generally  used.  The  two  most  useful 
sizes  for  students  are  "  half  imperial,"  measuring  about 
16  in.  x  23  in.  x  f  in.  thick,  suitable  for  elementary  work, 
and  "  imperial,"  32  in.  x  23  in.  x  J  in.  for  more  advanced 
work ;  professional  draughtsmen  nearly  always  use  a 
larger  size,  "  double  elephant,"  28  in.  x  41  in.,  but  this 
size  is  seldom  required  by  students.  The  drawing  board 
may  readily  be  made  by  a  joiner,  although  it  is  hardly 
possible  to  obtain  such  well-seasoned  and  suitable  material 
as  that  used  by  the  leading  firms  of  instrument-makers. 

The  best  boards  are  made  of  American  yellow  pine,  free 
from  knots,  square  jointed  and  battened  at  the  back,  the 
battens^fixed  with  domed  screws  sunk  in  slots  and  working 
on  brass  plates,  to  allow  for  swelling  and  shrinking  of  the 
board.  In  some  makes  the  backs  are  grooved  to  prevent 

8 


MAKING    DRAWING    BOARDS  9 

warping,  as  shown  in  Fig.  I  (the  under  side  of  a  battened 
drawing  board)  and  in  the  enlarged  detail,  Fig.  2  ;  and  the 
working  edge  (left-hand  end)  inlaid  with  an  ebony  slip  to 
prevent  wear  of  the  softer  pine. 

A  cheaper  kind  is  the  clamped  board,  Figs.  3  and  4.  These 
are  not  so  reliable  as  the  above,  for  the  shrinkage  of  the  panel 
causes  the  ends  of  the  clamps  to  project,  and  if  the  square 
is  used  from  that  edge  a  faulty  line  is  produced.  They  will, 
however,  answer  the  purpose  of  beginners  for  some  time,  if 
they  are  trued  up  occasionally,  and  they  are  much  cheaper 
than  the  battened  variety. 

A  very  reliable  form  of  board,  which  the  author  designed 
for  his  own  use  some  years  ago,  is  shown  in  Fig.  5.  It  is 
easy  to  make,  and  has  the  advantage  that  both  sides  of  the 
board  may  be  used,  and  there  is  no  possibility  of  the  panel 
splitting.  The  board  is  glued  up  and  cleaned  off  to  the 
required  size,  then  the  ends  are  grooved  exactly  one-third  of 
the  thickness.  Two  clamps  of  hard-wood,  straight-grained 
mahogany  for  preference,  about  the  same  thickness  as  the 
board,  are  prepared  with  a  similar  groove  to  that  in  the 
board,  when  these  are  fitted  on  as  shown,  just "  hand-tight," 
they  will  allow  the  board  to  swell  or  shrink,  but  prevent  it 
casting.  Of  course  they  must  be  fitted  with  dry  joints — • 
that  is,  not  glued.  The  depth  of  the  working  edge  must  be 
a  trifle  more  than  the  thickness  of  the  stock  of  the  T-square 
used. 

A  useful  attachment  to  the  board,  which  the  joiner 
student  can  make  for  himself,  is  the  "  copy  "  holder  shown 
in  Figs.  6  and  7.  These  may  be  two  thin  strips  of  mahogany, 
one  attached  directly  to  the  back  edge  of  the  board  by  means 
of  a  round-headed  screw,  the  other  pivoted  similarly  to  a 
short  block  or  fillet,  equal  in  thickness  to  the  opposite  slip, 
and  fixed  to  the  board  so  that  the  first  slip  folds  down  within 
it,  whilst  the  second  folds  over  the  first.  They  should  work 
stiftly,  and  the  edge  of  the  board  and  the  fillet  should  be 
bevelled  to  throw  the  holders  backwards  when  open. 
A  tilting  bar  (see  Fig.  6),  about  18  in.  x  2  in.  x  2  in.  is 


io  DRAWING    SQUARES 

useful  for  tilting  the  board  up  at  a  convenient  angle  for 
work. 

The  T-Square,  Figs.  8  and  9,  is  used  chiefly  for  drawing 
horizontal  lines.  It  should  be  of  the  same  length  as  the 
board  used,  and  those  with  tapering  blades  are  to  be  pre- 
ferred. The  stock  should  be  rebated  and  chamfered  as 
shown  in  the  enlarged  detail,  Fig.  io,  so  that  if  the  paper 
overhangs  the  board  it  will  not  throw  the  square  out  of  place. 
The  chamfering  prevents  the  set  square  catching  upon  the 
edge,  should  the  stock  lie  out  of  level.  The  blade  should 
be  screwed  to  the  stock,  and  in  the  larger  sizes  do  welled 
also,  as  shown  in  Fig.  io,  but  not  glued,  as  it  is  necessary 
to  take  it  off  for  re-shooting  at  times.  The  top  edge  should 
be  chamfered  down  to  T\  in.  thick,  so  that  lines  may  be  seen 
easier,  also  to  reduce  the  risk  of  irregular  lines  through 
alteration  of  the  angle  at  which  the  pencil  is  held.  Many 
draughtsmen  use  a  square  which  has  a  strip  of  celluloid  sunk 
in  the  working  edge  (see  Fig.  n) ,  as  lines  can  be  seen  through 
it ;  it  is  chiefly  of  service  when  inking-in  large  drawings. 

Set  Squares,  Figs.  12  and  13,  are  triangles  used  in  con- 
junction with  the  T-square  for  drawing  vertical,  perpen- 
dicular and  parallel  lines  at  any  angle.  They  are  made  of 
various  shapes,  materials  and  sizes.  The  most  useful  sizes  and 
shapes  are  those  known  as  45°  and  60°,  and  from  4  in.  to  8  in. 
in  height.  The  45°  square,  Fig.  12,  is  the  triangular  half  of  a 
true  geometrical  "  square"  ;  one  angle  is  a  right  angle,  the 
other  two  contain  45  degrees  each,  between  the  adjacent 
edges.  The  60°,  Fig.  13,  has  angles  of  90°,  30°  and  60°  respec- 
tively, and  it  might  as  rightly  be  termed  "30°,"  but  is  gener- 
ally described  as  above.  They  are  made  in  hard- woods, 
vulcanite  and  celluloid.  Wood  is  not  to  be  recommended  ; 
it  alters  in  shape  and  has  to  be  too  thick  to  be  manageable  : 
exception  may  be  made  to  this  general  statement  in  the 
case  of  "  framed  "  or  open  squares  made  of  hard -wood  with 
the  edges  chamfered  upon  one  side.  These  are  expensive. 
Celluloid  is  the  most  useful,  as  it  can  be  seen  through,  a  great 
advantage  in  elaborate  drawings,  but  it  has  a  serious  draw- 


12  FRENCH    CURVES 

back,  it  casts  freely  in  warm  weather,  and  thus  will  rise 
from  the  paper  in  places,  allowing  the  pencil  to  slip  under 
and  make  an  irregular  line.  It  may  be  restored  to  shape  by 
dipping  in  hot  water  and  placing  under  a  weight.  Vulcanite 
is  cheaper  and  stands  well,  but  is  liable  to  break  if  dropped  ; 
probably  it  is  the  most  popular  material. 

Architectural  or  French  Curves,  Fig.  14.— These 
are  shaped  pieces  of  thin  pear-wood  or  celluloid,  cut  into 
various  circular  or  elliptic  designs  for  the  purpose  of  guiding 
the  inking  pen  when  drawing  curved  lines.  Their  use  with 
the  pencil  is  to  be  deprecated,  as  tending  to  discourage  that 
freedom  of  hand  necessary  for  good  draughtsmanship. 
Their  methods  of  use  will  be  dealt  with  in  the  next  chapter. 

Instruments. — There  are  to  be  found  in  the  shops  that 
deal  in  artists'  and  students'  requirements  an  immense 
variety  of  these  "  tools  "  and  appliances,  and  the  inex- 
perienced reader  of  a  maker's  catalogue  is  bewildered  by  the 
numerous  varieties  of  the  same  instruments  shown  therein, 
and,  without  advice  from  an  experienced  draughtsman,  is 
very  likely  to  make  a  wrong  selection.  Many  of  the  instru- 
ments shown  are  only  of  service  to  specialists ;  others  are 
merely  time  savers,  the  work  they  are  designed  to  execute 
being  within  the  capacity,  with  a  little  skill  on  the  part  of 
the  user,  of  much  lower-priced  instruments  of  general  utility. 
With  the  former  it  is  not  the  purpose  of  this  book  to  deal. 
Only  those  things  that  may  be  considered  necessary  for  the 
ordinary  workman  student's  purpose  will  be  described.  It 
would  be  useless  attempting  to  indicate  what  prices  should 
be  paid,  as  tastes  will  differ  as  to  the  design  of  instruments. 
This,  with  the  quality  and  amount  of  finish  given  to  them, 
has  considerable  influence  upon  the  cost.  All  that  can  be 
stated  in  this  direction  is  that  the  higher  priced  article  is 
generally  the  cheaper  in  the  long  run — that  is,  it  will  remain 
in  good  order  the  longest  time.  British-made  instruments 
are  usually  more  reliable  than  foreign  made,  and  they  should 
be  purchased  either  from  the  makers  or  dealers  who  specialise 
in  these  things  rather  than  from  the  ordinary  stationers  or 


COMPASSES    AND    DIVIDERS  13 

second-hand  shops ;    these  latter  are  pretty  sure  to  stock 
"shoddy"  foreign -made  goods. 

Compasses. — These    are    instruments    for    describing 
circles.    There  are  several  varieties  ;  only  a  few  of  the 
more  generally  useful,  however,  are  described  here.     The 
commonest  form  is  that  known  as  a  "  half  set,"  Fig.  15, 
which  consists  of  a  pair  of  legs  of  which  one  point  is  remov- 
able, and  may  be  replaced  by  a  pencil  leg  or  "  point/'  or  by 
a  pen  or  "  ink  point/'  c,  Fig.  15,  as  they  are  termed  in  cata- 
logues and  a  "  lengthening  bar/'  a,  Fig.  15,  this  last  is 
inserted  into  the  socket  of  the  compasses  and  the  pen  or 
pencil  point  inserted  into  the  other  end  of  the  bar,  for  de- 
scribing circles  of  large  radius.     Some  instruments  are  fitted 
with  movable  needle  points.    These  are  too  fragile  for  the 
inexperienced  student's  use  and  should  be  avoided  ;  so  also 
should  those  compasses  having  triangular  "  points,"  which 
make  large  holes  in  the  paper  and  are  difficult  to  set 
accurately.     Round  hard  steel  points  fixed  into  the  legs  are 
the  best,  as  shown  at  b,  Fig.  15,  and  there  should  be  a  joint 
in  the  socket  leg  to  enable  the  pen  point  to  be  set  perpendicu- 
larly in  the  paper  when  the  legs  are  opened  out  widely ; 
preferably  there  should  be  a  joint  in  each  leg,  as  this  con- 
siderably increases  the  working  "  span."    The  usual  sizes 
of  these  instruments  are  4J  in.,  5  in.  and  6  in.   long. 
When  only  a  half  set  can  be  purchased,  and  the  small 
instruments  mentioned  subsequently  are  not  obtained  until 
advanced  work  is  attempted,  the  medium-size  set  will  be 
found  the  most  serviceable,  but  if  complete  equipment  is 
obtained  at  the  start,  choose  the  largest  size  in  compasses 
and  smallest  in  dividers  and  spring  bow. 

In  choosing  compasses  perhaps  the  chief  point  to  note  is 
the  fit  of  the  joints  ;  the  legs  should  move  "  sweetly," 
without  any  jerk.  Socketed  joints  should  slide  together 
tightly  without  shake  throughout ;  and  all  joints  should 
have  screwed,  not  riveted  pivots. 

Dividers. — These  are  compasses  with  solid  or  non- 
removable legs  ;  they  are  used  for  taking  and  transferring 


14  RULING    PEN 

dimensions,  for  stepping  off  series  of  equal  dimensions,  and 
—as  their  name  suggests — for  dividing  dimensions,  etc.,  into 
various  numbers  of  parts  by  trial. 

For  advanced  work  a  variety  termed  "  hair  spring  "  is 
to  be  preferred.  These  have  the  point  of  one  leg  attached 
to  a  spring  controlled  by  a  small  milled  head  screw.  The 
coarse  adjustment  is  made  in  the  usual  way  by  pressure  of 
the  finger  on  the  legs,  then  very  minute  final  adjustment  is 
made  by  turning  the  screw-head. 

Bow  Compasses,  Fig.  16. — These  are  smaller  and 
lighter  than  the  full-size  instruments.  They  are  made  in 
sets  of  three,  having  fixed  pen,  pencil  and  divider  points,  and 
are  of  two  sizes,  3  in.  and  3j  in.  long.  These  are  very 
convenient  for  describing  smaller  circles  and  curves. 

Bow-Springs,  Fig.  17,  are  miniature  compasses  also 
made  in  sets  of  three.  The  legs  are  formed  of  spring  steel 
and  are  normally  open  to  their  greatest  radius  about  |-  in., 
but  may  be  closed  by  turning  the  milled  head  screw  to  de- 
scribe circles  down  to  -f^  in.  radius.  They  are  usually  sold  in 
sets  in  velvet-lined  cases,  but  single  bows  are  also  supplied. 
They  are  useful  for  drawing  very  small  circles  and  curves. 

The  Beam  Compasses. — These  are  pen  and  pencil  legs, 
inserted  into  brass  sockets,  which  are  then  adjusted  upon 
a  lath  or  rod,  called  the  "  beam/'  They  are  used  for 
describing  circles  of  greater  radius  than  the  compasses  will 
extend.  Fig.  18  shows  a  home-made  arrangement  in 
mahogany  that  will  be  readily  understood  upon  inspection. 

The  Ruling  Pen,  or,  as  it  is  often  miscalled,  drawing  pen, 
Fig.  19,  for  it  is  quite  unsuitable  for  drawing  in  the  usual 
sense  of  the  term,  consists  of  a  pair  of  adjustable  steel  nibs 
fixed  to  a  straight  handle.  The  better  sorts  have  one  of  the 
nibs  hinged  to  enable  it  to  be  more  thoroughly  cleaned,  and 
to  permit  the  removal  of  the  burr  formed  on  the  edges  when 
resharpening.  Its  use  will  be  described  fully  later,  and  it 
need^only  be  said  here  that  it  is  used  with  a  straight  or 
curved  ruler  for  inking-in  pencilled  lines. 
The  Parallel  Rule,  Fig.  20,  is  an  instrument  for 


PROTRACTORS  15 

drawing  one  line  parallel  with  another,  to  which  one  edge  of 
the  rule  is  applied.  It  is  of  rather  limited  use,  and  requires 
considerable  care  in  manipulation.  It  is  superseded  for 
students'  use  by  the  pair  of  set  squares  as  described  on 
page  25. 

Protractors. — These  are  instruments  for  measuring 
and  setting  out  angles.  There  are  two  forms,  the  circular 
or  semicircular,  and  the  rectangular.  They  are  made  of 


Fig.  I.     Semicircular  Protractor 


gfl 
"j 

0  0 

I>Q 

m 

i  i  /  ' 

A     z 

4   y  -.  ^ 
^  3f 

•1 

I  -    H 

m 

• 

a,    • 



^a 
°  " 

WH  

So 

I.    -      - 

Fig.  2.     Rectangular  Protractor  and  Scale 

various  materials — boxwood,  ivory,  bone,  brass,  etc. 
Although  differing  greatly  in  appearance,  the  two  forms  are 
set  out  or  divided  in  exactly  the  same  manner,  as  will  be 
seen  by  inspection  of  Fig.  2,  whereon  a  part  of  the  describing 
semicircle  is  shown,  with  the  divisions  radiating  from  the 
centre,  a  few  of  these  are  dotted-in  in  each  figure  to  indicate 
the  principle  of  dividing  the  instrument,  which  may  be 
briefly  explained  thus  :  A  circle  of  any  diameter  is  divided 
upon  its  circumference  into  360  equal  parts,  lines  are  drawn 
from  these  points  to  the  centre,  and  each  division  thus  formed 


16  DRAWING    PAPERS 

is  said  to  contain  one  degree,  and,  obviously,  any  other 
circle  described  upon  the  same  centre  will  be  divided  into 
the  same  number  of  degrees  by  these  radiating  lines,  there- 
fore it  does  not  matter  what  size  circle  or  protractor  is  used, 
the  number  of  degrees  contained  between  any  two  lines 
forming  an  angle  will  be  accurately  shown  by  it,  and  on  the 
instrument  these  are  numbered  for  easy  reference,  com- 
mencing at  the  diameter  of  the  circle  :  in  the  example  only 
each  tenth  degree  is  numbered,  and  a  few  of  the  intermediate 
degrees  shown  (note,  degrees  are  usually  indicated  by  a  small 
circle  over  the  figure  thus,  30°).  The  semicircular  instru- 
ment contains  only  half  of  360° — viz.  180°.  For  con- 
venience of  reference  the  degrees  are  numbered  from  i  to 
180,  in  both  directions,  that  they  may  be  read  off  readily 
from  either  hand.  Upon  the  straight  edge  of  the  semi- 
circular and  the  plain  edge  of  the  rectangular  protractor 
in  the  middle  of  its  length,  is  placed  an  index  mark  which 
indicates  the  centre  of  the  circumscribing  circle.  When  it 
is  desired  to  measure  an  angle,  the  instrument  is  laid  with 
its  edge  upon  one  side  of  the  angle,  and  the  aforesaid 
centre  mark  at  the  vertex  or  intersection  of  the  sides,  then 
the  number  of  degrees  contained  between  the  two  sides  of 
the  angle,  will  be  indicated  on  the  edge  of  the  protractor 
where  the  second  side  intersects  it.  In  like  manner  an  angle 
is  laid  off  on  any  given  line  by  placing  the  straight  edge  of 
the  protractor  on  the  line,  ticking  off  the  required  angle  close 
to  the  edge,  marking  the  central  or  index  point,  and  drawing 
the  second  side  between  the  two  points  marked.  The  scale 
shown  in  the  middle  of  Fig.  2  is  explained  under  Scales, 
page  22. 

MISCELLANEOUS   DRAWING   ACCESSORIES 

Drawing  Paper. — Of  this  there  are  several  kinds  ;  for 
elementary  work  "  cartridge  "  paper  is  the  most  suitable, 
but  a  smooth  or  nearly  smooth  surfaced  kind  should  be 
chosen.  A  rough-surfaced  or  coarse-grained  paper  causes 


PENCILS  17 

the  point  of  the  pencil  or  pen  to  wear  down  quickly,  and 
the  production  of  lines  of  a  regular  depth  or  thickness  be- 
comes, if  not  an  impossibility,  a  work  of  great  difficulty. 
Paper  should  be  purchased  from  dealers  in  artists'  materials, 
and,  if  unobtainable  locally,  may  be  ordered  by  post  from 
well-known  houses  such  as  Reeves  &  Sons,  Moorgate  Street ; 
Rowney  &  Son,  Oxford  Street,  w. ;  Winsor  &  Newton, 
Newman  Street,  w. ;  B.  J.  Hall  &  Co.,  Victoria  Street,  s.w. ; 
all  of  London,  who  will  supply  quires  of  twenty-four  sheets 
or  single  sheets  at  slightly  increased  prices.  For  advanced 
work,  or  important  drawings  that  will  have  a  deal  of 
handling,  a  superior  quality  of  paper,  called  hand-made,  is 
advised.  These  are  known  by  their  various  makers'  names, 
such  as  Whatmans',  Harding's,  Hollingsworth's,  Turkey 
Mill,  etc.  Hand-made  papers  are  of  varying  grades,  accord- 
ing to  their  smoothness  of  surface ;  those  most  frequently 
used  are :  H.P.,  "  hot-pressed  " — the  smoothest,  best  for 
inked  line  drawings,  but  taking  colour  only  moderately 
well;  N.,  signifying  natural  grain  —  not  hot-pressed, 
sometimes  described  as  "  Not  " — slightly  rough  surface, 
the  ordinary  article  for  general  use ;  and  R.  "  Rough  " — 
good  for  colouring  upon,  but  practically  useless  for  fine  or 
mechanical  drawing. 

The  standard  sizes  of  drawing  paper  most  used  are: 
royal,  25  in.  x  20  in. ;  imperial,  30  in.  x  22  in.,  and 
double  elephant,  40  in.,  x  27  in.  Of  these  the  most 
economical  size  is  "  imperial,"  which  may  be  cut  into 
halves  to  form  half  imperial,  22  in.  x  15  in.,  a  very  con- 
venient size  for  elementary  practice. 

Drawing"  Pencils  are  made  of  about  twelve  degrees  of 
hardness,  but  practically  only  four  are  in  general  use  by 
architectural  draughtsmen  and  students,  indicated  by  the 
letters  F,  H,  HB  and  B.  The  choice  of  these  must  be 
left  to  the  individual,  as  they  must  be  selected  according 
to  the  "  touch  "  of  the  draughtsman.  Beginners  may  well 
start  with  H  and  HB,  the  first  for  "pointing  off "  dimensions, 
construction  lines,  etc.  ;  the  second  for  "  lining-in  "  or 


1 8  ERASERS 

finishing  the  drawing  when  it  is  not  intended  to  ink  it.  B 
is  serviceable  for  shading  and  freehand  work,  but  as  the 
various  makers'  "  degrees  "  differ,  the  selection  should  be 
made  by  experiment.  When  a  suitable  pencil  is  found, 
the  same  brand  should  be  adhered  to  always.  It  may  be 
added  that  no  pencil  sold  for  less  than  a  penny  need  be 
expected  to  give  satisfactory  work,  and  higher  priced  ones 
are  cheaper  in  the  end,  as  they  last  longer.  The  hexagon 
shape,  a,  Fig.  i,  page  26,  is  the  best  to  use,  as  it  will  not  roll 
off  the  sloping  board.  Special  small  pencils  are  made  to 
fit  various  compasses ;  but  the  author  personally  prefers 
to  split  down  a  piece  of  ordinary  size  pencil  and  extract 
the  lead,  which  is  then  rolled  up  in  a  strip  of  paper,  pasted 
or  gummed  until  the  right  size  is  obtained  to  fit  the  holder. 
These  "  paper  "  pencils  are  easier  to  keep  in  order  than  the 
wood-cased  ones,  and  the  same  depth  of  tone  can  be  ob- 
tained in  the  curves  as  in  the  other  parts  of  the  drawing. 
The  best  way  to  sharpen  these  is  to  wrap  a  narrow  strip 
of  fine  glass  paper  around  the  point,  then  revolve  the  pencil 
between  the  thumb  and  finger. 

Rubber  is  used  for  erasing  pencil  lines ;  only  a  "  soft  " 
kind  should  be  used,  so  that  the  surface  of  the  paper  is  not 
destroyed.  Square  blocks  are  used  for  extensive  altera- 
tions and  cleaning,  and  Wedge-shaped  pieces  for  small 
erasures.  On  no  account  should  a  hard  rubber,  or  so-called 
"  ink  eraser,"  be  used,  as  this  destroys  the  surface  of  the 
paper,  so  spoiling  the  appearance  of  the  drawing.  Drawing 
that  requires  considerable  cleaning  should  be  rubbed  over 
with  slightly  stale  or  dry  bread  crumb,  the  palm  of  the  hand 
being  used  for  the  purpose. 

Drawing  Pins,  Fig.  21,  p.  n. — These  are  used  for 
securing  the  paper  to  the  board ;  medium  sizes  are  the 
best,  and  those  with  domed  or  bevelled  heads  which  allow 
the  T-square  to  pass  over  them  without  catching.  The 
perfect  drawing  pin,  however,  has  yet  to  be  invented. 
Most  of  those  in  use  are  injurious  either  to  the  paper,  the 
board  or  the  finger  nails,  also  to  the  temper  of  the  user. 


DRAWING    INKS  19 

The  pin  lift,  Fig.  22,  page  n,  is  useful  for  extracting 
stubborn  pins. 

Ink. — The  ink  used  in  architectural  drawing  is  a  special 
kind  that  will  not  corrode  the  instruments.  It  is  usually 
called  Indian  ink,  but  is  really  made  in  China  (that  is,  the 
genuine) .  This  requires  to  be  rubbed  up  in  water  in  a  saucer 
— the  bottom  of  an  ordinary  tea  saucer  can  be  utilised  if 
the  proper  one  is  not  at  hand — it  is  rubbed  up  similarly  to 
cake  colours. 

Only  sufficient  for  use  at  the  time  should  be  mixed,  as  it 
dries  quickly  and  becomes  gritty  if  remoistened  after  dry- 
ing in  the  saucer.  A  little  indigo  either  from  the  domestic 
"  blue  "  bag  or  artists'  water-colour  mixed  in  the  liquid 
improves  and  intensifies  the  black.  Various  liquid  "  Indian  " 
and  waterproof  inks  in  bottles  are  now  prepared  and 
stocked  by  dealers  ;  these  are  convenient  when  much 
inking-in  has  to  be  done.  They  are  also  useful  for  drawings 
that  have  to  be  coloured,  as  this  kind  of  ink  will  not  wash 
up,  but  it  is  rather  difficult  to  use  in  fine  pens,  as  it  dries 
rapidly  and  clogs  the  pen,  which  requires  constant  cleaning 
or  replacing.  The  author  keeps  a  phial  of  water  at  hand, 
into  which  the  pen  can  be  dipped  occasionally. 

Tracing  Paper  and  Cloth. — This  is  specially  prepared 
paper  or  linen  which  is  semi-transparent.  When  placed 
over  a  drawing,  the  lines,  etc.,  can  be  seen  through  it, 
and  easily  copied  or  "traced"  with  pencil  or  pen.  It  is 
supplied  in  sheets  20  in.  x  30  in.  and  30  in.  X  40  in., 
also  in  rolls  of  various  widths  and  about  21  yards 
long. 

Scales  are  instruments  of  wood,  metal,  cardboard, 
etc.,  having  one  or  more  faces,  upon  which  are  engraved  or 
printed  a  number  of  equal  divisions  and  subdivisions,  which 
may  represent  yards,  feet,  inches,  etc.,  as  determined. 
They  are  used  to  set  off  dimensions  upon  drawings  to  any 
desired  reduction  in  size  of  the  original  or  object  repre- 
sented. 

When  a  drawing  is  made  of  the  same  dimensions  as  the 


20  CONSTRUCTING    SCALES 

object  it  represents  it  is  said  to  be  drawn  "  full  size,"  when 
made  smaller,  it  is  said  to  be  drawn  "  to  scale."  Such  a 
drawing  must,  if  it  is  to  be  used  again  for  obtaining  accurate 
measurements  of  the  object,  be  made  proportionately 
throughout — that  is,  every  part  of  it  must  be  drawn  to  the 
same  scale,  and  it  is  to  ensure  this,  in  technical  drawings, 
that  carefully  prepared  "  scales  "  are  used.  The  majority 
of  scales  are  made  I  foot  long  ;  but,  of  course,  may  be  of 
any  other  length  the  maker  or  user  chooses,  and  they  may 
bear  from  two  to  a  dozen  different  scales  on  their  faces. 
For  students'  drawing  purposes,  cardboard  scales  with  not 
more  than  one  scale  at  each  edge  are  to  be  preferred,  as 
with  these  there  is  less  likelihood  of  mistakes  arising  through 
using  the  wrong  scale.  It  is  often  necessary  to  set  out  a 
scale  upon  a  drawing,  as  a  suitable  one  may  not  be  upon  the 
instrument  in  the  possession  of  the  draughtsman,  and  in 
important  drawings,  the  scale  should  always  be  drawn 
first  upon  the  paper  and  worked  from,  then  any  alteration 
in  the  size  of  the  sheet  due  to  atmospheric  conditions  will 
not  affect  the  measurements,  as  the  scale  will  alter  in  the 
same  ratio  as  the  drawing,  whilst  an  independent  scale 
might  not. 

On  page  21  are  shown  five  different  scales  suitable  for 
laying  down  on  drawings  and  as  many  different  ways  of 
drawing  them  ;  these  details  differ  with  the  taste  of  the 
draughtsman.  Fig.  i  is  a  scale  of  J  in.  to  the  foot,  and  is 
made  long  enough  to  measure  12  feet.  Anything  drawn 
to  this  scale  would  be  ^  of  the  real  size  of  the  object  repre- 
sented, because  there  are  forty-eight  quarter  inches  in  a 
foot,  and  Jg-  is  called  the  representative  fraction  of  the 
scale,  or,  shortly,  "  the  fraction." 

Fig.  2  is  a  scale  of  J  in.  to  a  foot ;  the  fraction  being  ¥\. 

Fig.  3  is  J  in.  to  the  foot,  the  fraction  being  ^.  Fig. 
4  is  i  J  in.  to  the  foot  or  J  the  real  size  ;  because  there  are 
eight  one  and  a  half  inches  in  a  foot,  and  as  the  representative 
fraction  of  this  scale  is  J,  care  must  be  taken  when  reading 
instructions  not  to  confuse  it  with  inch  to  a  foot.  This 


SCALES 


21 


is  a  favourite  workshop  scale,  as  the  common  2-foot  rule 
can  be  used,  calling  the  ~  in.  divisions  thereon  inches, 


7          2          3        4         f>         C,         7         8         9        W        11       12  Ft 


I        I       I 


I       I       I       I       I       I 


fig.  I.  Seal*  of  &"  to  JF*  or  &  *? 

I    I   [H    IIP  ill  W  I    I    1  4*  1    i  I??  1    11 


/E0r.  ^.  .£«*&*  flT  Jff  c/t  to  /^t  or  iff 

01234 


Sculo  cr     inch  tc  tcvt 
O 


IF* 


4.  Scaled'  Is  inch  to  foot  or  $W 


i<*.  7. 


Fig.  6.  **<?  J. 

Figs,  i  to  5.  Architectural  Scales.     Fig.  6.  Method  of  dividing  a  Scale 
Fig.  7.  Workshop  Method  of  dividing  a  Line  into  Equal  Parts 


and  each  ij  in.  a  foot.     Fig.  5  is  a  scale  of  3  in.  to  i  ft. 
or  one-fourth  full  size ;  the  representative  fraction  is  J. 

The  most  common  scales  in  architects'  offices  are  \  in., 
J  in.,  3  in.  and  full   size.     Engineers'   draughtsmen  use 


22  DIAGONAL    SCALES 

these  also  :  f  in.,  f  in.  and  I J  in.  to  a  foot  and  sometimes 
6  in. — i.e.  half-full  size — perhaps  the  worst  possible  scale  to 
work  to,  as  it  is  fruitful  of  errors. 

In  laying  down  a  scale,  the  feet,  to  the  required  fraction, 
should  be  set  off  with  the  dividers  upon  a  line  near  the 
bottom  of  the  drawing  paper,  and  the  divisions  drawn  in  by 
the  aid  of  the  set  square,  and  numbered  towards  the  right 
hand,  starting  at  the  second  division  ;  the  first  one  marked 
o,  is  reserved  for  inch  subdivisions.  In  the  larger  scales, 
these  may  be  set  off  with  the  dividers  direct  ;  but  in  the 
smaller  ones,  it  is  better  to  adopt  the  method  shown  in 
Fig.  i,  and  enlarged  in  Fig.  6.  Set  up  a  line  at  any  con- 
venient angle  from  the  left  extremity  of  the  line  to  be 
divided,  and,  opening  the  dividers  to  any  convenient  space, 
wider  than  the  required  division,  step  it  up  the  inclined 
line  until  twelve  (or  any  other  number  required)  spaces  are 
marked.  From  the  twelfth  point,  draw  a  line  to  the  right- 
hand  extremity  of  the  line  to  be  divided,  as  point  b  in  Fig. 
6.  Next  draw  a  series  of  parallel  lines  to  this  one  from  the 
other  points,  and,  where  they  intersect  the  horizontal  line, 
erect  short  perpendiculars,  which  will  represent  inches  in 
this  case.  This  is  a  rapid  and  accurate  method  of  dividing 
any  line.  A  favourite  workshop  method  by  aid  of  the  2-foot 
rule  is  shown  in  Fig.  7.  Draw  two  parallel  lines  at  right 
angles  to  the  line  to  be  divided,  as  at  c  and  d,  which  shows 
aline  7J  in.  long,  that  is  to  be  divided  into  nine  equal  parts ; 
lay  the  rule  across  the  lines  with  the  extremity  on  one  line, 
and  the  required  number  upon  the  other,  tick  off  the  inches, 
with  a  pencil ;  then  draw  parallels  to  the  first  two  through 
the  points  to  cut  the  line  c-d. 

The  Diagonal  Scale  shown  on  the  protractor,  Fig.  2, 
p.  15,  is  used  for  taking  very  minute  measurements.  The 
one  shown  will  measure  to  two  decimal  places,  or  the 
hundredth  part  of  one  of  the  large  or  primary  divisions, 
which  may  represent  inches,  feet,  yards,  chains,  etc.,  as 
required. 

It  is  constructed  by  drawing  a  rectangle  whose  height  is 


READING    SCALES  23 

generally,  but  not  necessarily,  equal  to  the  length  of  one  of 
the  primary  divisions,  1-2-3-4  saY  one  inch,  then  draw  nine 
parallel  lines,  dividing  the  rectangle  into  ten  equal  spaces. 
Divide  the  left-hand  primary  at  top  into  ten  equal  parts  ; 
these  will,  of  course,  in  this  case,  represent  tenths  of  an  inch. 
Divide  the  bottom  line  similarly,  and  draw  lines  diagonally 
from  one  division  at  the  top  to  the  next  one  at  the  bottom. 
Now  the  lower  end  of  each  line  has  moved  one-tenth  of  an 
inch  to  the  left  in  its  passage  across  the  rectangle,  and  as 
it  is  itself  divided  into  ten  equal  parts,  each  of  these  parts, 
counting  from  the  top,  is  ^  of  J^,  or  TJo  of  a  primary 
nearer  the  left  than  the  one  immediately  above  it.  Thus, 
if  it  is  desired  to  measure  2-24  in.,  place  the  dividers  with 
one  leg  on  the  primary  2,  on  the  horizontal  line  4  as  at  a, 
and  stretch  it  out  along  the  line  until  it  reaches  diagonal  2, 
as  shown  by  the  dot.  Any  other  decimal  part  may  be  found 
similarly,  always  reading  the  units  on  the  vertical  lines, 
the  tenths  on  the  diagonal  lines  and  the  hundredths  on  the 
horizontal  lines. 


CHAPTER   III 

GENERAL    INSTRUCTIONS    AND    HINTS 
ON   DRAWING 

How  to  Fix  the  Paper.  Finding-Marks — damp-stretching. 
Using  the  Squares.  To  draw  Parallel  Lines.  Sharpening 
the  Pencil.  Lining-in.  Managing  the  Ruling  Pen.  Inking-in. 
Curved  Lines.  To  keep  Drawings  Clean.  Where  to  Commence 
a  Drawing — how  to  proceed.  Examinations — how  to  draw, 
what  to  avoid.  Laying  off  Dimensions.  To  Measure  Curved 
Lines.  Managing  the  Compasses.  Locating  Centre  of  Circles. 
Draughtsmen's  Lines  and  Signs.  Sections.  Standard  List  of 
Material  Hatchings 

Fixing  the  Drawing  Paper  for  elementary  work. — The 
paper  is  usually  secured  to  the  drawing  board  by  means 
of  drawing  pins  at  the  corners  (see  Fig.  i,  page  25).  If  the 
paper  cockles,  on  account  of  its  stiffness  or  through  rolling 
up,  fix  first  a  pin  at  top  and  bottom  edges  near  the  middle, 
then  smooth  the  paper  out  with  the  hand,  one  side  at  a  time, 
and  pin  the  corners,  thus  making  it  lie  quite  flat.  If  it  has 
to  be  removed  from  the  board  before  the  drawing  is  finished, 
a  short  pencil  mark  should  be  made  on  the  paper  at  each 
extremity  of  the  edge  of  the  T-square,  and  these  marks 
made  to  coincide  with  the  edge  of  the  square  when  refixing. 
This  ensures  parallelism  in  subsequent  lines  (see  /-/,  Fig. 
i,  p.  25) .  Students  at  technical  schools,  etc.,  who  may  have 
to  use  a  different  board  on  each  evening,  should  invariably 
place  these  "  finding  marks  "  on  the  paper  immediately 
on  laying  it  down.  For  elaborate  drawings,  or  those  that 
have  to  be  coloured,  it  is  better  to  damp-stretch  the  paper  ; 
this  is  accomplished  by  turning  down  a  margin  all  round 
the  sheet  of  about  f  of  an  inch,  then  sponging  over  the 

24 


DRAWING    PARALLELS  25 

remaining  portion  with  clear  water  until  the  paper  is  uni- 
formly damp,  when  the  dry  margins  are  covered  with  paste 
or  glue,  then  turned  over  and  rubbed  down  on  the  board, 
where  they  are  left  until  dry,  when  the  paper  will  shrink, 
producing  a  tight  and  very  smooth  surface  to  work  upon. 
Thick  papers  are  better  wetted  all  over,  including  the 
margins,  before  pasting. 

Method  of  Using  the  Squares. — The  T-square  must  be 
manipulated  with  the  left  hand — that  is,  it  is  moved  up  and 
down  the  left  edge  of  the  board  only. 
If  it  is  used  on  more  than  one  edge, 
and  the  board  should  happen  to  be 
out  of  square,  all  the  main  lines  of 
the  drawing  would  be  wrong.     All 
horizontal  lines  should  be  drawn  by 
aid  of  the  T-square  and  all  vertical 
lines  with  the  set  square  ;  this  en-  ^  Method     of     drawing 

,,  v    •  j«      i  Parallel      Lines     at     any 

sures  them  being  perpendicular  to  inclination 
each  other.     (It  may  be  as  well  here 

to  point  out  that,  geometrically,  there  is  a  difference  between 
a  vertical  and  a  perpendicular  line,  though  these  terms  are 
often  used  as  if  they  were  synonymous.  A  perpendicular 
line  is  one  at  right  angles,  or  "  square  "  to  any  other  line, 
and  obviously  may  lie  in  any  position  on  the  paper,  whilst 
a  vertical  line  is  one  at  right  angles  to  a  horizontal  or  level 
line  and  therefore  must  be  always  upright.)  If  the  vertical 
line  to  be  drawn  is  longer  than  the  set  square,  move  the 
T-square  up  or  down  as  required,  keeping  the  finger  and 
thumb  of  the  right  hand  on  the  set  square,  and  blade  of  the 
T-square  respectively,  to  prevent  lateral  movement.  Should, 
however,  this  occur,  the  line  can  be  continued  unbroken 
by  placing  the  pencil  on  the  part  already  drawn,  then  moving 
the  set  square  along  until  its  edge  touches  the  pencil,  when 
the  line  can  be  continued. 

Inclined  Parallel  Lines  may  be  drawn  at  any  distance 
apart  by  placing  one  edge  of  a  set  square  to  the  given  line, 
or  at  any  desired  inclination  (as  at  a,  illustrated  above),  then 


26  USING    PENCILS 

bringing  a  second  square  close  up  to  another  edge,  as  shown 
at  b.  The  first  square  may  then  be  moved  up  or  down  as 
required,  as  shown  in  dotted  lines,  when  the  other  two  edges 
will  be  constantly  parallel  to  their  original  positions.  A 
more  extended  range  of  movement  may  be  obtained  by 
using  the  edge  of  the  T-square  as  a  guide  on  which  to 
move  the  set  square  to  its  successive  positions,  as  in- 
dicated at  c  and  d,  where  the  full  lines  represent  those  to 
be  drawn. 

The  T-square,  especially  when  polished,  has  an  annoying 
habit  of  slipping  off  the  sloping  board.  This  may  be  checked 
by  passing  a  small  rubber  band — such  as  is  used  for  fastening 
rolls  of  paper — around  the  blade  near  the  stock. 

Sharpening  Pencils. — This  should  be  done  neatly  and 
carefully  with  a  sharp  penknife  or  chisel ;  good  work  can 
never  be  done  with  a  blunt  or  irregularly 
sharpened  pencil.  For  ruling  straight 
lines  a  chisel-shaped  "  point  "  or  edge  is 
advocated  by  some,  similar  to  b  and  c, 
adjacent  Fig.  For  freehand  work,  setting 
off  lengths,  or  for  use  with  French  curves, 
a  long  conical  point  should  be  used  as 
shown  at  a. 

.  Use  the  pencil  lightly.    Do  not   "  en- 

Methods  of  Pointing:  »i  ,«.  A.  •        11 

Pencils  grave      the  paper,  nothing  looks  worse 

(a)  Conical  Point    on  a  drawing  than  a  network  of  white 

(f)  and  (c)  Chisel  marks  or   furrows  that  once   contained 

pencil  lines.     It  would  be  a  counsel  of 

perfection  to  advise  that  no  false  lines  should  be  drawn. 

These  may  be  looked  upon  as  inevitable  with  a  beginner, 

but  he  need  not  draw  undue  attention  to  his  errors  or 

tentative  attempts. 

When  a  drawing  is  to  be  finished  in  pencil,  the  preliminary 
construction  may  be  made  with  a  hard  pencil,  which  will 
make  a  faint  line,  easily  removable.  After  the  drawing  is 
complete  and  found  to  be  correct,  remove  superfluous  ends 
to  the  lines,  with  the  rubber,  and  go  carefully  over  the 


METHOD    OF    INKING    DRAWINGS 


27 


entire  drawing  with  a  softer  pencil.    This  operation  is  called 
"  lining-in." 

Inking-in. — If  the  drawing  is  to  be  finished  in  ink,  it 
is  advisable  to  draw  every  line  first  in  pencil,  and  to  carry 
the  ends  beyond  their  intersections,  as  otherwise  it  is 
difficult  to  see  where  to  stop  the  pen  when  the  ruler  lies 
over  the  lines.  After  the  inking-in  is  finished  the  pencil 
lines  can  be  removed  with  soft  rubber  or  bread  crumbs. 

The  method  of  holding  a  ruling  pen  when  inking  a  line  is 
illustrated  here.  It  is,  of  course,  held  in  the  right  hand,  with 
the  pen  upright  or  nearly  so,  and  the 
forefinger  resting  upon  the  setting 
screw.  The  precise  height  of  the 
hold  is,  of  course,  a  matter  of  taste, 
and  is  also  dependent  upon  the  length 
of  the  pen.  The  pen  should  have 
the  ink  rising  about  §  in.  between 
the  nib,  which  must  be  screwed  up 
until  the  desired  gauge  of  line  is  ob- 
tained. This  should  be  tried  on  a  spare 
piece  of  paper — not  the  margin  of  your 


Method  of  holding  the 
Ruling  Pen 


drawing — and  once  the  pen  is  set,  it  should  not  be  altered 
until  all  the  lines  of  that  depth  are  finished.  Hold  the  rule 
or  straight  edge  (which  should  have  a  slight  under  bevel, 
as  shown,  to  prevent  the  ink  adhering  and  causing  a  blot), 
firmly,  with  fingers  spread  out  ;  this  latter  seems  such  an 
obvious  precaution  as  to  be  needless  to  mention,  but  for 
the  fact  that  the  author  has  sometimes  spoiled  a  drawing 
himself  by  neglecting  it.  When  the  draughtsman  is  intent 
upon  drawing  his  line  correctly,  he  is  apt  to  relax  the  pres- 
sure with  the  left  hand,  then  disaster  follows  swiftly. 
Curved  lines  other  than  circular  are  best  inked-in  by  the 
aid  of  French  curves,  as  shown  in  Fig.  I,  p.  28,  where  the 
grained  portion  indicates  one  end  of  a  "  curve,"  placed  so 
as  to  coincide  with  the  portion  of  the  line  between  a  and 
b,  the  dotted  line  indicating  the  curve  reversed  to  mark 
in  from  c-d.  The  connection  b-c  is  made  at  a  third  adjust- 


28  WHERE    TO    COMMENCE 

ment,  and  a  fourth  adjustment  enables  the  part  d-e  to 
be  drawn,  the  fully  inked  line,  a~b-c~d-e,  representing  the 
finished  line  obtained. 

In  joining  circular  to  straight  lines  it  is  better  to  draw  the 
circular  ones  first,  and  connect  the  straight  ones  to  them 
exactly  at  the  springing  points  as  shown  at  B,  Fig.  2,  on  this 
page.  This  avoids  the  unsightly  breaks  in  the  continuity 
of  the  lines  shown  at  A,  Fig.  2,  in  which  the  straight  lines 
were  drawn  first. 

When  removing  pencil  lines,  rub  in  the  direction  of  the 


Fig.  2.  Right  and 
Wrong  methods  of 
joining  Straight  to 

Fig.     i.     Method    of    inking-in          Curved  Lines 
Curved  Lines 

lines,  not  across  them,  and  clean  the  rubber  of  lead,  on  a 
piece  of  coarse  linen,  frequently. 

Keeping"  the  Drawing  Clean. — Beginners  always  have 
a  difficulty  with  this.  The  soiled  appearance  of  their 
pencilled  drawings  is  due  to  the  squares  taking  up  a  little 
of  the  blacklead  when  passing  over  the  lines  and  depositing 
it  where  it  is  not  wanted.  To  prevent  this,  wipe  them 
occasionally  with  a  piece  of  linen  and,  when  lining-in,  pass 
a  clean  sheet  of  paper  (tissue  or  tracing  paper  is  best,  as  it 
can  be  seen  through)  over  the  parts  finished,  so  that  the 
hand  or  instruments  shall  not  cause  smudging. 

Where  to  Commence  a  Drawing.— This  depends  some- 
what on  the  nature  of  the  drawing.  When  making  a  number 
of  simple  exercises  or  small  separate  drawings,  commence 


EXAMINATION    WORK  29 

at  top  left-hand  corner,  and  work  across  the  sheet  horizont- 
ally, then  work  downwards.  This  avoids  continually  going 
over  the  finished  work  with  the  squares.  In  copying  from 
examples  such  as  are  given  in  this  book,  or  in  designing 
original  work,  plans  should  be  drawn  first,  then  sections, 
and  finally  the  elevations  projected  from  the  two  former. 

Do  not  fill  in  all  the  details  or  hatch  sections  as  you  go 
in  any  one  part  of  a  set  of  drawings,  but  get  in  the  chief 
members,  etc.,  first,  in  each  of  them  ;  this  will  localise  many 
of  the  interior  lines  and  prevent  overrunning,  also,  in  case  of 
alterations,  will  save  much  time. 

In  making  drawings  at  examinations  where  speed  is 
essential,  position  on  the  sheet  is  not  of  much  moment,  but 
the  solution  should  be  commenced  by  putting  in  the  skeleton 
or  outline  of  the  problem  as  indicated  in  the  question,  and 
filling  in  such  details  as  suggest  themselves,  and  as  time 
permits.  Always  avoid  repeating  exactly  similar  parts  and 
confine  your  attention  to  important  constructive  features, 
rather  than  minute  details.  For  example,  if  asked  to  draw 
a  partition,  do  not  spend  two-thirds  of  the  time  carefully 
spacing  and  drawing  in  a  series  of  studs,  all  of  which  are 
exactly  alike,  but  draw  in  all  the  main  timbers  first,  or  even 
half  of  them  if  the  two  sides  are  alike,  finally  putting  in  a 
few  studs  to  inform  the  examiner  that  you  know  they  should 
be  there.  Again,  if  you  are  drawing  a  ledge  door  it  is  more 
important  to  show  the  proper  position  of  the  braces  than  it 
is  to  indicate  nail-heads  in  the  ledges.  The  examiner  will 
assume  you  know  that  the  door  is  to  be  nailed  together 
if  you  show  him  that  you  know  how  the  members  are 
arranged. 

In  Laying  Off  Dimensions  it  is  better  to  use  scales 
than  dividers,  but  if  the  latter  are  used  do  not  prick  holes 
in  the  paper  with  them — this  spoils  the  appearance  of  any 
drawing — but  lay  the  dividers  sideways  to  the  line,  and 
tick  off  their  points  with  the  pencil.  Do  not  lay  off  dimen- 
sions from  one  another  successively,  but  measure  from  a 
common  point  either  at  the  end  or  middle  of  the  line  or 


3o  MEASURING    CURVES 

member.  In  the  first  method  an  error  at  one  point  is  re- 
peated throughout,  whilst  in  the  second  it  is  confined  to  the 
original  point  and  is  readily  located. 

Measuring  Curved  Lines. — It  is  often  necessary  to  do 
this  with  accuracy  when  a  stretch-out  or  development  of  the 
surface  is  required.    The  best  method 
is  to  set  the  spring  bow  dividers  with 
a  small  opening,  varying  with  the 
—    quickness  of  the  curve,  and  stepping 

Method   of  obtaining   the    jt      j  th      curved    line,    counting 

Length  of  a  Curved  Line 

how  many  steps  are  required  to  reach 

from  end  to  end,  then  transferring  to  a  straight  line  a  like 
number  of  steps.  It  is  not  necessary  to  divide  the  curve 
exactly  into  equal  parts.  If  the  last  step  overpasses  the  end, 
mark  where  it  reaches  and  lay  off  the  same  number  of  steps 
on  the  straight,  then  come  back  and  set  the  dividers  exactly 
to  the  space  exceeded,  and  mark  this  within  the  last  mark 
or  step  (see  Fig.  above,  where  the  straight  line  contains  the 
sixteen  divisions  of  the  curved  line). 

The  Stretch-Out  of  a  semicircle  may  be  approximately 
obtained  by  drawing  lines  through  the  ends  of  the  diameter 
at  an  angle  of  60°  with  the  same, 
as  shown.  The  set  square  may  be 
utilised  as  indicated  by  dotted 
lines,  then  drawing  a  line  tangent 
to  the  curve  and  parallel  to  the 
diameter  as  A-B  which  will  be 
very  nearly  the  length  of  the 
curved  line. 

When    describing    Circles  f 

..,.-,  ,     u     .v       Obtaining  Length  of  a  Semi- 

with    the    compasses,    hold    the  circle 

instrument  lightly  between  finger 

and  thumb  as  near  the  top  as  possible,  to  avoid  closing  the 
legs  and  revolve  steadily,  to  avoid  piercing  the  paper.  If  a 
number  of  concentric  circles  have  to  be  described  make 
a  cross  on  a  thin  piece  of  card  and  mark  similar  crossed 
lines  on  the  drawing.  Make  the  two  sets  of  lines  coincide. 


DRAUGHTSMEN'S    SIGNS  31 

This  will  locate  the  centre,  and  the  compasses  may  be  used 
on  the  card  without  damaging  the  drawing. 

A  piece  of  celluloid  is  sometimes  used  instead  of  the  card, 
as  the  centre  can  be  seen  through  it.  Describe  the  smallest 
circles  first,  as  revolving  the  compass  at  an  angle  when 
opened  wide  enlarges  the  hole. 

Draughtsmen's    Lines  and   Signs.— It  is   desirable 
for  the  benefit  of  those  having  to  read  drawings  that  a  simple 
and    uniform    system    of 
lines    should   be   used   in  ~*2 

preparing   them — that  is, . — 3 

for  example,  a  dotted  line     * 

should  not  be  used  in  one -  - 5 

drawing  where  a  full  line  A —  M 

would  be  used  in  others.        »«--/-3  — -*-/0'-+ z-4 *7 

From  an  inspection  of     ~"~  *      "*  ~~="~/o 

a  quantity  of  work  turned  Lines  and  signs  used  by  Draughtsmen 
out  by  leading  draughts- 
men I  conclude  that  the  following  list  most  nearly  represents 
prevailing  practice. 

The  Fine  Line  (No.  i)  is  used  for  all  interior  and  inferior 
ines  in  a  drawing. 

The  Full  or  Heavy  Line  (No.  2)  for  outlines  or  bound- 
aries. Note,  the  line  should  be  of  a  regular  thickness 
throughout,  the  extent  of  which  will  depend  upon  the  scale 
of  the  drawing,  and  it  should  not  be  as  shown  in  No.  3,  uneven 
and  irregular. 

The  Dotted  Line  (No.  4)  for  hidden  parts,  or  parts 
out  of  the  plane  of  section  upon  which  the  drawing  is 
made. 

The  Chain  or  Break  Line  (No  5)  is  generally  used  to 
indicate  a  proposed  new  position  in  the  object  which  is 
shown  in  full  line,  or  vice  versa  ;  it  is  also  used  in  lieu  of 
dotted  lines  where  the  latter  might  be  confused  with 
projectors. 

Projectors  are  always  dotted  when  left  upon  a  drawing, 
which  occurs  seldom,  except  for  teaching  purposes.  In 


32  DRAUGHTSMEN'S    LINES 

ordinary  work  they  are  rubbed  out  after  the  inking-in  is 
completed. 

The  Dot  and  Dash  Line  (No.  6)  is  invariably  used  to 
indicate  line  of  section,  accompanied  by  a  capital  letter 
at  each  extremity  for  reference.  It  is  also  used  with  an 
abbreviated  dash,  for  paths  of  a  moving  portion,  such  as 
a  door. 

Dimension  Lines  (No.  7)  are,  as  their  name  indicates, 
intended  to  guide  the  eye  along  the  route  of  a  dimension. 
They  are  a  variety  of  the  break  line  with  longer  intervals 
and  shorter  dashes,  the  object  being  to  make  them  as  un- 
obtrusive as  possible,  subject  to  their  ready  indication  of 
the  extremities  of  the  dimension  located  by  arrow  heads. 
Usually  in  architectural  drawings  they  are  made  in  blue 
ink  and  centre  lines  are  made  in  red. 

The  Broken  or  Irregular  Line  (No.  8)  isused  to  indicate 
that  the  drawing  or  part  on  which  it  occurs  is  much  longer  or 
wider  than  is  shown,  the  real  dimension  being  specified  in 
figures.  The  object  of  so  breaking  a  drawing  is  to  curtail 
its  space,  and  is  a  common  practice  in  preparing  "  rods  "  or 
other  full-size  drawings  in  so  far  as  widths  are  concerned. 
Upon  rods,  the  length  is  never  broken  ;  to  do  so  would  render 
the  rod  useless  for  setting-out  from. 

The  False  Line  (No.  9)  is,  as  shown,  "  false  "  in  two 
senses,  as  both  the  line  to  be  removed  and  the  indicated 
line  should  rightly  be  in  pencil,  which,  of  course,  is  im- 
possible in  a  printed  example.  When  making  a  drawing 
of  any  importance  a  number  of  tentative  lines  may  be 
necessary  ;  again,  the  inexperienced  draughtsman  will  place 
lines  where  he  does  not  intend  them.  It  is  not  always  the 
best  thing  to  erase  these  at  once.  Quite  frequently  they  may 
be  utilised,  and  constant  use  of  the  rubber  damages  the 
paper,  so,  when  a  false  line  is  made  in  pencil  which  is  not 
intended  to  be  inked-in,  the  draughtsman  does  not  rub  it 
out  at  once,  but  "  scribbles  "  it  out,  as  shown,  only  in  pencil ; 
and  all  vanishes  with  the  final  cleaning-off. 

Sometimes  it  is  found  necessary  to  dot  a  line  which  it 


MATERIAL    SECTIONS 


33 


was  first  intended  to  draw  full.  In  this  case  do  not  rub  it 
out,  but  "  herring  bone  "  it  as  shown  in  No.  10,  of  course 
again  in  pencil  only. 

Sectioning  or  Hatching. — The  method  of  indicating 
various  materials  by  special  hatchings  is  again  coming  into 
use  by  the  professional  draughtsman,  in  consequence  of  the 
facility  with  which  uncoloured  line  drawings  may  be  re- 
produced by  the  various  sun-printing  and  other  processes. 
When,  however,  only  one  or  a  few  copies  are  required,  the 
drawings  are  much  clearer  to  read  if  the  various  materials 
are  distinguished  by  colouring  the  sections,  but  as  it  is  of 


Brick       Stone         Wood       Wrotlron   Cast  Iron       Zinc        Glass£ 


Steel        Lead         Brass       Concrete    Earth        Plaster     Glass  S 
Hatchings  for  Materials 

little  service  describing  colours  without  reproducing  them, 
these  instructions  are  confined  to  black-ink  sectioning. 
The  chief  conventional  hatchings  are  shown  and  described 
above. 

It  must  be  understood  that  these  various  hatchings  are 
to  be  applied  to  parts  in  "  section  "  only.  "  Graining,"  to 
indicate  wood  in  elevation,  should  be  indulged  in  very 
sparingly;  its  copious  use  indicates  the  amateur  draughtsman 
who  thus  hopes  to  hide  his  faults  of  design  or  construction. 
Technical  drawings  are  not  intended  to  be  pictures,  and 
they  should  indicate  their  meaning  clearly,  definitely  and 
economically.  A  few  deft  touches  with  the  pen  to  indicate 
direction  of  the  grain  or  to  distinguish  wood  from  space  is 
all  that  is  permissible  or  desirable. 


34  MATERIAL    SECTIONS 

TECHNICAL    DRAUGHTSMEN'S    STANDARD   LIST   OF  MATERIAL 

HATCHINGS  (see  Page  33) 

Brick. — Medium  ruled  lines  at  an  angle  of  45°  with 
chief  dimensions,  not  too  closely  drawn. 

Stone. — Similar  lines  alternately  with  dotted  or  broken 
lines. 

Wood. — Lines  slightly  curved  drawn  freehand,  repre- 
senting the  annual  rings.  Large  timbers  are  indicated  by 
a  few  radiating  "  shakes."  Adjacent  pieces  should  be 
distinguished  by  drawing  the  lines  in  reverse  directions. 

Wrought  Iron. — Alternate  thick  and  thin  lines  ruled 
at  an  angle  of  45°. 

Cast  Iron. — Closely  ruled  lines  at  angle  of  45°  with 
main  dimension. 

Steel. — Broken  fine  lines  at  45°. 

Lead. — Reversed  medium  lines  or  "  cross  hatching." 

Brass. — Dot  and  dash  lines  perpendicular  to  longest  side. 

Zinc. — Heavy  black  ruled  lines  at  45°  to  longest  direction. 

Glass. — Longitudinal  ruled  fine  lines. 

Glass  in  Elevation. — Diagonal  ruled  lines,  lightened  or 
erased  with  the  rubber  irregularly  to  give  effect  of  broken 
light. 

Concrete. — Irregular  curved  shapes  and  dashes. 

Earth. — Interlaced  cross  hatching  in  patches. 

Plaster. — Points  of  ink  or  splashes. 

Small  Sections  in  Metal,  when  it  is  not  desired  to 
indicate  any  special  kind,  are  put  in  solid  black. 


CHAPTER  IV 
LETTERING   DRAWINGS 

Objects  and  Requirements  in  Lettering.  Faults  the  Beginner 
should  avoid.  The  Relative  Sizes  for  Titles.  The  chief 
Types  of  Letters.  Names  and  Characteristics  —  Roman, 
Stone,  Block,  Italics,  Egyptian,  Stump.  Numerals.  Alphabets. 
Details  of  Lettering — necessity  of  uniform  size,  how  to  obtain  it. 
The  Proper  Slope.  Balance — how  to  ensure  it.  Proportion  of 
Letters.  Spacing — its  difficulties.  What  to  aim  at  to  obtain 
Uniformity.  Optical  Corrections.  Points  of  Detail.  Right 
and  wrong  methods  of  forming  Letters.  Tools  to  use 

THE  proper  lettering  of  technical  drawings  is  a  matter  of 
almost  equal  importance  with  the  preparation  of  the  drawings 
themselves.  By  the  term  "  lettering  "  is  meant  the  writing 
in  of  titles,  reference  notes,  numerals,  directions,  etc.,  upon 
drawings. 

Various  other  terms  have  been  used  to  describe  this 
operation,  including  titling,  writing,  printing,  noting,  etc. 
None  of  these  seem  correctly  or  comprehensively  to  describe 
the  operation.  "  Lettering  "  would  appear  to  come  nearest 
to  an  accurate  definition,  as  we  must  first  form  letters  before 
we  can  obtain  words. 

Letters  and  alphabets  have,  in  their  fundamental  char- 
acteristics, a  conventional  or  orthodox  form  which  it  is  not 
wise  to  depart  from  too  widely.  It  may  be  taken  for 
granted  that  the  object  aimed  at  in  lettering  drawings  is 
to  make  the  drawing  plainer  or  more  understandable  to  the 
reader,  and  anything  that  detracts  from  this  object  is  obvi- 
ously out  of  place,  however  artistically  interesting  or  curious 
it  may  be  in  itself. 

A  certain  amount  of  freedom  and  individuality  of  style  is 
not  only  allowable  but  is  desirable,  and  adds  to  the  beauty 

35 


36  LETTERING    DRAWINGS 

and  interest  of  a  drawing,  but  beginners  especially,  should 
guard  against  a  tendency  to  produce  grotesque  caricatures 
of  letters,  under  the  mistaken  idea  that  unfamiliar  shapes 
are  necessarily  artistic.  Before  one  can  "  invent  "  new 
designs  in  letters,  the  history  of  their  evolution  or  develop- 
ment must  be  studied,  when  it  will  be  found  that  there  is  a 
reason  for  the  shapes,  characteristics  and  proportions  that 
have  become  conventionalised. 

This  is  not  the  place  to  consider  the  evolution  of  alphabets 
with  a  view  to  their  improvement.  We  must  be  satisfied 
with  providing  a  suitable  type  of  lettering  for  technical 
drawings,  as  adopted  by  expert  draughtsmen  in  the  best 
architectural  and  engineering  offices  at  the  present  time,  and 
to  describe  the  readiest  and  most  workmanlike  methods  of 
producing  them. 

The  beginner  would  do  well  to  confine  himself  to  one  or 
other  of  the  alternative  examples  given,  and  to  acquire  a 
thorough  mastery  of  the  particular  type  chosen  before 
attempting  to  produce  a  style  of  his  own. 

It  will  be  as  well  to  remember  that,  whilst  ugly,  careless, 
illegible  lettering  will  spoil  the  appearance  of  the  best  and 
most  accurate  drawing,  a  badly  executed  drawing  is  made 
no  more  acceptable  by  being  well  lettered. 

The  characteristics  of  the  style  chosen  should  be  noted, 
and  the  common  fault  of  using  two  or  more  different  styles 
in  the  same  word  or  line  should  be  avoided.  For  instance, 
it  would  be  wrong  to  use  the  "  a  "  of  No.  3,  page  37,  with  the 
styles  shown  in  Nos.  n  and  13,  or  say,  the  "  e  "  of  No.  5 
with  type  No.  8 

The  use  of  many  types  or  even  different  sizes  of  the  same 
type  of  letter  on  a  drawing  is  to  be  deprecated,  as  conveying 
a  sense  of  unrest  to  the  observer.  Good  draughtsmen 
usually  content  themselves  with  three,  or,  at  the  most,  four, 
sizes  of  letters  upon  one  drawing  :  "  large"  for  the  main 
heading,  "  medium  "  for  sub-titles  and  "  small  "  for  details. 
When  a  note  calling  special  attention  to  some  particular 
part  is  required,  a  special  type  is  used,  quite  different  from 


tfl 


. 

N 
"K 


*3 


be     «    .S> 

**** 


^ 


I 

LN 


!  H 

m 

(^r 

iffil 


bK 


OD 


«B*B*-8< 

^    n    ^N 

S  y  I 


38  DESCRIPTION    OF   TYPE 

the  rest,  as  shown  at  No.  n,  page  37.  The  terms  "  large," 
"  medium  "  and  "  small "  are,  of  course,  purely  relative,  and 
not  indicative  of  the  size  (see  Fig.  13,  page  37).  The  actual 
sizes  of  the  letters  chosen  must  depend  upon  the  size  of  the 
drawing  or  its  scale,  and  no  hard  and  fast  rule  can  be  given 
for  this,  as  so  much  depends  on  circumstances,  but  as  some 
guide  to  the  beginner  it  may  be  stated  that  the  "  heading  " 
No.  2,  if  made  twice  the  size  printed,  or  say  J  in.  high, 
would  be  a  suitable  size  for  double  elephant  drawing  sheets 
— -i.e.  40  in.  x  27  in.,  and  No.  7  made  •£$  in.  high  would 
be  suitable  for  headings  upon  imperial  sheets. 

Before  entering  into  the  details  of  spacing  and  the  forma- 
tion of  letters,  it  will  be  as  well  to  give  the  technical  names  of 
the  various  types  illustrated,  and  draw  attention  to  their 
characteristics.  It  may  also  be  pointed  out  that  the  terms 
used  here  are  those  of  draughtsmen  and  lithographers. 
Printers  and  sign  writers  in  some  cases  use  different  terms  ; 
so  also  do  stone  and  metal  engravers.  In  fact,  the  nomen- 
clature of  alphabets  is  somewhat  chaotic,  and  it  is  deemed 
advisable  to  adhere  to  those  definitions  commonly  used  by 
modern  technical  draughtsmen  and  map  makers. 

Roman  (No.  i). — -This  example  shows  two  sizes  of 
capitals  termed  by  printers,  "upper  case  "  letters,  and  further 
defined  by  them  as  "  caps,  and  small  caps."  The  terms, 
"  upper  case  "  and  "  lower  case,"  which  are  now  getting 
into  text-books,  are  printers,  or  rather  compositors',  terms 
indicating  capital  type  letters  and  small  type  letters,  and 
these  do  not  indicate  any  special  style  of  letter.  For  con- 
venience of  composing,  the  small  letters,  which  are  most 
frequently  required,  are  placed  in  a  case  close  to  the  operator, 
and  those  less  frequently  required — i.e.  capitals — -in  a  case 
above  ;  hence  the  terms,  upper  and  lower  case. 

The  characteristics  of  Roman  type  are  that  the  letters 
are  upright,  and  have  "  serifs  "  or  projections  beyond  the 
limb  of  the  letter.  Originally  the  serif  was  a  fine  line  used 
for  the  purpose  of  cutting  off  or  squaring  the  ends  of  the 
stroke.  Serifs  are  employed  in  other  types,  but  in  the 


TYPES  39 

Roman  they  are  always  joined  to  the  limb  by  curved  lines. 
The  limbs  of  the  curved  letters,  B,  R,  S,  etc.,  swell  in  the 
middle  of  the  stroke,  the  up  and  terminal  strokes  of  the 
others  being  fine. 

Stone  (No.  2). — This  is  a  purely  modern  ornamental 
letter,  shaded  on  one  side,  and  is  technically  known  as 
"  open  " — -i.e.  the  limbs  are  bounded  by  two  fine  lines  with- 
out ink  or  colour  between.  If  partially  filled  in  with  dot 
and  curve  as  shown  it  becomes  "  ornamented  open  stone." 
In  this  type  the  serif  is  of  substantial  proportions. 

Italics  (No.  3). — Also  termed  sloping  Roman.  This 
is  one  of  the  easiest  types  to  form  with  the  writing  pen. 
Originally  it  was  the  printers'  imitation,  in  type-letters,  of 
handwriting,  which  is  naturally  sloping.  It  was  first  used 
by  the  Italian  printers,  hence  the  term,  "  italics."  If  these 
small  letters  were  made  upright  they  would  then  be  termed 
lower-case  Roman. 

Block  (Nos.  4,  6  and  7),  also  called  sanserif — i.e. 
without  serifs — is  of  three  varieties :  "  solid,"  as  No.  4 ; 
"  open,"  as  No.  7,  and  "  sloping,"  as  No.  6  ;  the  latter  is 
shown  also  with  a  variation  known  as  "  half  filled."  The 
essentials  of  this  type  are  that  all  the  limbs  should  be  of 
equal  thickness  and  that  the  various  limbs  join  each  other  at 
right  or  acute  angles — -i.e.  they  do  not  flow  into  each  other 
by  easy  curves  as  do  the  Roman,  but  join  up  abruptly.  It 
is  a  purely  mechanical  type  of  letter,  but  none  the  less  useful 
on  that  account. 

Egyptian  (No.  5),  also  known  as  black  letter,  is 
generally  used  on  technical  drawings  in  conjunction  with 
"  block  "  reference  letters,  as  shown  in  the  example.  The 
ruling  of  the  heavy  line  below,  as  shown  in  Nos.  4  and  5, 
though  now  usual  in  modern  offices,  is  not  invariable.  It 
should  be  confined  to  more  important  sub-titles  that  are 
desired  to  "  leap  to  the  eye  "  immediately  on  inspection. 
No.  ii  is  termed  "sloping  Egyptian."  The  characteristic 
of  this  type  is  that  the  letter  is  made  of  equal  thickness 
throughout. 


40  DETAILS    OF    LETTERING 

Stump  (No.  8). — This  is  quite  a  modern  and  clean- 
cut  type  of  lettering  not  greatly  differing  from  italics,  but 
more  nearly  approaching  cursive  or  running-hand  :  its 
principal  characteristic  is  that  each  letter,  though  made 
in  "flowing"  style,  finishes  abruptly  without  connection 
with  its  neighbour,  which  gives  it  much  distinctness. 

The  lettering  of  the  plates  throughout  this  book  is  in 
"  stump." 

The  Numerals.— No.  9  is  Egyptian.  No.  10,  originally 
termed  Arabic,  is  now  frequently  called  Roman.  The  real 
"  Roman  "  type,  in  which  letters  are  used  as  figures,  is  but 
seldom  adopted  in  the  drawing  office. 

Details  of  Lettering. — It  is  most  essential  that  the 
letters  in  a  word  or  series  of  words  should  be  of  uniform  size 
and  accurately  in  line.  This  does  not  imply  that  each 
letter  shall  occupy  exactly  the  same  space,  for  that  is 
obviously  impossible  if  we  consider  the  various  shapes  of 
letters,  but  that  letters  similar  in  shape  shall  be  similar  in 
size  throughout :  and  symmetry  for  the  whole  group  of 
letters  is  then  obtained  by  judicious  spacing,  which  is 
dealt  with  farther  on.  Take,  for  example,  the  word  "  Eleva- 
tion," type  No.  3.  It  will  be  found  by  trial  with  the  dividers 
that,  leaving  the  serifs  out  of  consideration,  such  letters 
as  n,  a,  e  and  v  are  all  of  one  size ;  so  also  are  i,  t  and  /, 
but  these  do  not  occupy  so  much  space  as  the  former 
letters.  Such  letters  as  C,  D,  G,  0,  etc.,  will  also  be 
similar  in  size,  but  occupying  more  space  than  either  of 
the  former. 

To  ensure  uniformity  in  height  and  alignment,  it  is  neces- 
sary to  rule  lines  locating  the  tops  and  bottoms  of  the  letters, 
as  shown  in  the  examples  by  dotted  lines  ;  these,  of  course, 
will  be  done  in  pencil  when  copying,  to  be  rubbed  out  after 
the  letters  are  inked  in.  There  is  a  school  of  faddists  who 
decry  the  ruling  of  lines  or  the  use  of  any  mechanical  aids 
to  accuracy  as  tending  to  destroy  the  "  freehand  "  ability 
of  the  draughtsman. 

These  extremists,  however,  have  few  if  any  disciples 


INCLINATION    OF    LETTERS  41 

among  practical  draughtsmen  ;  the  waste  of  time,  especially 
by  novices,  in  obtaining  anything  like  satisfactory  results 
without  such  assistance,  places  this  absolute  freehand 
method  outside  practical  consideration.  A  slavish  copying, 
or  entire  reliance  upon  set  squares  and  rulers  is  not  here 
advocated,  but  judicious  use  of  them  as  aids  to  the  be- 
ginner is  recommended.  With  letters  of  types  No.  2  or 
No.  7,  four  guide  lines  may  be  used ;  their  object  will  be 
obvious  upon  inspection.  Where  capitals  and  small 
capitals,  as  in  Nos.  I  and  6,  or  capitals  and  "  lower  case  " 
letters,  as  in  Nos.  3-5  and  8  are  used,  three  lines  are  required. 
There  are  so  few  letters  with  "  tails  "  that  it  is  seldom 
necessary  to  use  a  line  for  them ;  slight  irregularity  in 
these  is  less  noticeable  than  with  the  tops  or  rising 
limbs. 

Solid  block,  as  No.  4,  and  numerals,  as  Nos.  9  and  10, 
require  two  lines  only.  The  choice  of  upright  or  sloping 
letters  is  mainly  one  for  individual  taste,  but  whichever  is 
adopted,  the  same  style  should  be  adhered  to  throughout, 
with  numerals  to  match. 

The  slope  or  inclination  to  be  given  is  also  largely  a 
matter  of  taste.  Too  great  an  inclination  should  be  avoided, 
as  this  conveys  the  impression  that  the  letters  are  falling 
over.  Some  few  draughtsmen  use  the  60°  set  square  as  a 
guide,  but  in  the  author's  opinion  this  gives  rather  too 
much  leaning,  and  he  suggests  65°,  as  indicated  in  Fig.  13, 
page  37,  as  more  suitable  for  general  work. 

Balance. — The  symmetrical  letters,  or  those  with  double 
inclined  limbs,  as  A,  V,  W,  X,  Y,  Z,  and  the  curved  letters, 
as  C,  G,  O,  Q,  should  have  neither  limb  arranged  to  the 
common  slope,  but  a  line  passing  through  the  middle  of 
the  letter  should  lie  in  the  slope,  as  indicated  in  Fig.  12, 
where  the  right  and  wrong  method  of  balancing  the  letter 
A  is  shown,  as  an  example  of  what  to  do  and  what  to 
avoid. 

Proportion. — It  has  already  been  pointed  out  that  the 
letters  as  a  whole  must  be  made  proportionate  to  the  size 


42  ALPHABETS 

of  the  sheet  they  are  to  occupy ;  large  letters  should  be 
used  for  main  headings  or  titles  ;  important  sub-headings 
should  be  of  medium  size,  and  details,  which  may  be  numer- 
ous, should  be  of  a  smaller  size.  The  relative  size  of  either 
of  these  classes  is  shown  in  the  diagram,  Fig.  13,  p.  37. 
In  addition  to  this  some  attention  must  be  given  to  the 
proportion  of  parts  in  the  letters  ;  otherwise  the  result  will 
be  either  weak  and  ineffective  or  simply  absurd.  The 
proportions  adopted  in  these  examples  for  the  rising  limbs 
of  letters,  and  for  the  major  caps,  where  two  sizes  are  used, 
is  to  divide  the  total  height  intended  for  the  letters  into 
three  equal  parts,  allotting  two  parts  to  the  bodies  and 

ABCDEFGHIJKLM 
NOPQRSTUVWXYZ 

ab  cdefghijhlmn 
opqrstuvwxyz 

Typical  Alphabets — Roman  Capitals,  Italic  Smalls 

minor  caps  and  one  part  to  the  rising  limb  or  heads  as 
indicated  by  the  dotted  lines,  or,  in  the  case  of  major 
capitals,  carrying  these  up  to  the  third  part. 

The  Roman  and  block  letters  B,  R  and  S  should  be 
larger  or  heavier  at  the  bottom  part,  so  also  should  the 
numerals  3,  5,  6  and  8.  The  middle  bar  of  the  E,  F  and  H 
should  be  either  at  the  middle  of  the  height  or  slightly 
above  it,  never  below  :  on  the  contrary,  the  cross  bar  of 
A  and  lower  bar  of  P  must  be  below  the  middle. 

Spacing. — This  is  the  most  difficult  part  of  lettering 
which  the  inexperienced  draughtsman  will  have  to  over- 
come, and  it  is  with  the  object  of  assisting  him  in  this 
that  the  most  frequently  occurring  combinations  of  letters 
upon  architectural  drawings  have  been  chosen  for  examples, 


SPACING  43 

in  preference  to  a  series  of  complete  alphabets.  Two  of 
these  latter,  however,  have  been  given  for  reference. 

The  precise  shape  of  the  various  letters  is  of  less  moment 
than  the  preservation  of  the  main  characteristics  of  the 
type  and  the  judicious  arrangement  of  the  respective 
letters  into  words.  It  is  impossible  to  lay  down  any 
universal  rule  for  the  distance  apart  of  letters,  so  much 
depends  upon  circumstances. 

Generally  the  lettering  of  architectural  and  technical 
drawings  is  rather  closely  spaced,  whilst  that  of  maps, 
estate  plans  and  the  like  are  widely  spaced,  as  in  the  latter 
it  is  desirable  that  the  words  should  indicate  the  extent 
of  the  land,  etc.,  they  are  placed  upon,  or  refer  to.  Uniform 
rather  than  equal  spacing  should  be  aimed  at,  and  this  is 
best  obtained  by  so  arranging  the  letters  that  the  white 
space  or  voids  between  them  shall  be  approximately  equal 
in  area.  To  obtain  this  uniformity,  the  letters  must  be 
spaced  according  to  their  shape.  Thus,  referring  to  the  word 
Masonry,  No.  2  in  the  example,  it  will  be  found  that  al- 
though the  letters  appear  to  be  all  at  the  same  distance 
apart,  the  O  and  S,  for  instance,  are  actually  only  half 
the  distance  apart  that  the  N  and  the  R  are,  if  measured 
at  the  middle.  Two  letters  A  placed  together  would  need 
as  close  spacing  as  possible,  because  the  equal  and  opposite 
slopes  of  the  adjacent  sides  leave  a  relatively  large  white 
area  between  them.  The  P  in  type  3  needs  closer  spacing 
than  a  similar  R  would,  because  the  absence  of  the  lower 
limb  leaves  a  more  prominent  void.  It  will  thus  be  seen 
that  the  actual  spacing,  depending  upon  the  juxtaposition 
of  various  letters,  and  the  style  of  the  letters  themselves, 
must  be  left  to  the  judgment  of  the  draughtsman.  A 
preliminary  "  sketching  in  "  of  the  letters  faintly  is  ad- 
visable upon  the  space  it  is  proposed  to  allot  them.  This  is 
frequently  done  by  experienced  draughtsmen  on  a  spare 
piece  of  paper,  to  judge  of  the  effect  before  drawing  the 
letters  finally  in  position. 

Points   of  Detail. — If   the   various    O's    and   similar 


44  WRITERS'    TOOLS 

curved  letters  are  closely  observed  they  will  be  found  to 
project  slightly  above  and  below  the  line  of  the  other  letters  ; 
this  is  a  necessary  optical  correction.  If  they  are  made 
exactly  to  line,  they  will  appear  to  drop  or  look  smaller  than 
the  others.  This  will  perhaps  be  more  easily  realised  if  a 
square  of  I  in.  side  and  a  circle  of  i  in.  diameter  are  drawn 
side  by  side  and  level.  In  lettering  of  the  italic  type,  the  tops 
of  the  t's  should  be  shorter  than  those  of  1,  d,  b,  etc., 
and  the  f  should  be  made  without  a  dropped  tail  (see 
Fig.  i,  page  42).  It  is  somewhat  difficult  for  the  be- 
ginner to  decide,  when  forming  letters  of  the  italic  and 
similar  types,  which  to  make  the  heavy  limbs  in  the  capitals, 
such  as  M,  N,  W,  etc.  It  must  be  borne  in  mind  that  this 
type  is  based  upon  handwriting  or  "  script,"  and  that  in 
writing  with  the  pen,  up  strokes  are  made  light  to  avoid 
spurting  of  the  ink,  and  the  down  strokes  heavy  to  give 
emphasis  to  the  letter.  Now  take  M  for  example.  In 
writing  this  letter  we  commence  at  the  bottom,  carrying 
the  pen  up  with  a  light  stroke,  then  down  with  a  heavy 
one,  up  again  lightly  and  down  with  a  full  stroke.  N,  in 
like  manner,  commences  with  a  light  stroke,  down  or  across 
with  a  heavy  one  and  finishes  up  with  a  light  one.  All 
printers'  type  follows  this  order  of  procedure,  and  letters 
made  with  the  strong  strokes  or  limbs  in  reverse  order  look 
incongruous  and  amateurish. 

Tools. — Small  and  medium-size  letters  can  be  satis- 
factorily executed  with  a  quill  or  an  ordinary  J  pen.  For 
very  small  lettering  a  Gillot's  mapping  pen  is  useful.  For 
larger  work  a  writer's  brush  is  advisable  ;  a  "  Sable  "  No.  i 
would  be  suitable.  As  a  matter  of  fact,  all  the  letters  given 
in  the  examples  were  done  with  the  brush  in  the  original. 
Compasses  and  ruling  pen  may  be  used  by  beginners  for 
block  lettering,  but  of  course  it  can  be  done  much  more 
quickly  with  the  brush.  If  this  is  used,  the  letters  should  be 
carefully  pencilled  in  first,  then  gone  over  with  the  brush. 
Indian  ink  with  a  very  little  Prussian  blue  rubbed  up  in  it  is 
the  best  medium  to  work  in,  though  for  reproduction  pur- 


INKS  45 

poses  one  of  the  liquid  "  carbon  "  inks  is  generally  used,  as 
giving  a  more  intense  black.  Ordinary  writing  ink  should 
on  no  account  be  used,  as  it  is  too  fluid  to  give  sufficient 
depth  of  tone.  A  cardboard  set  square  cut  to  the  required 
"  pitch  "  will  be  found  useful  for  setting  out  the  sloping 
letters. 


CHAPTER    V 
ORTHOGRAPHIC    PROJECTION 

OR 

PRODUCTION  OF  PLANS,  ELEVATIONS  AND  SECTIONS 

Scope  of  the  Chapter — theory  of  orthographic  projection.  Projec- 
tion upon  three  Planes — Examples.  A  Dwarf  Cupboard — 
preparation  of  the  plan,  projecting  the  elevation,  determining 
the  section.  A  Field  Gate — how  to  draw  it.  Types  of  Roofs — 
Couple  and  Couple  Close,  Collar  bolt  and  tie,  King  Post ;  spac- 
ing of  trusses.  A  Laminated  Rib  Roof — details  of  construction, 
method  of  drawing.  Doors — framed,  ledged  and  braced,  con- 
struction of,  preparing  the  drawings.  Panelled  Doors — how 
specified.  A  Diminished  Stile  Door.  Floors — a  single  floor 
with  details,  arrangement  of  bridgers  and  trimmers.  Windows 
— Cased  Sash  frames,  common  and  superior,  constructional 
details,  method  of  drawing.  French  Casement  Frames — details 
of  construction.  Shop  Fittings — a  draper's  counter,  method 
of  construction.  Important  points  in  Technical  Drawing.  An 
Octagonal  Ogee  Roof — dimensions,  how  to  set  out  the  plan,  how 
to  obtain  moulds  for  ribs,  projecting  the  elevation.  Lantern 
Lights — definition  and  description  of,  an  examination  question, 
a  solution  with  details  of  construction.  A  Circle-on-Circle 
Entrance  Door  and  Frame — an  unusual  form,  instructions  for 
projecting  the  vertical  section ;  obtaining  soffit  mould,  face 
mould,  etc. 

IN  this  chapter  it  is  proposed  to  instruct  the  student,  by 
means  of  graduated  examples  of  various  objects  drawn 
from  the  field  of  carpentry,  joinery,  brickwork  and  masonry, 
how  to  prepare  plans,  elevations,  sections  and  details  of 
construction  of  several  parts  of  a  building  and  its  fittings, 
thus  enabling  him  to  reproduce  accurately  these  copies, 
as  well  as  more  advanced  ones  that  may  be  contained  in 
other  works. 

In  the  first  lesson  it  is  assumed  that  the  student  knows 

46 


48     MEANING    OF   ORTHOGRAPHIC   PROJECTION 

nothing  further  upon  the  subject  than  what  he  has  gained 
by  reading  the  general  instructions  in  Chapter  II.  In  the 
succeeding  lessons  the  more  elementary  instructions  are 
not  repeated,  the  notes  being  confined  to  new  points 
arising  out  of  the  increased  difficulties  of  the  examples. 
Therefore  it  will  be  necessary,  for  a  full  comprehension 
of  the  subject,  that  the  student  shall  work  through  the 
drawings  in  the  order  in  which  they  are  given.  In  no  case 
should  a  drawing  be  copied  to  less  than  twice  the  size  shown, 
and  the  more  intricate  ones  should  be  made  to  still  larger 
scale. 

It  will  perhaps  be  advisable,  before  entering  into  the  actual 
instructions  for  copying  and  producing  drawings,  to  explain 
briefly,  by  aid  of  diagrams,  the  theory  of  right-angled 
projection,  usually  distinguished  as  orthographic.  This 
term  is  derived  from  the  Greek,  "  orthographia  " — orthos, 
correct ;  grapho,  to  write — signifying  correct  writing.  In 
those  days  the  distinction  between  writing  and  drawing  was 
not  so  marked  as  now,  so  the  word  has  come  to  stand  for 
"  correctly  drawn  "  in  the  sense  that  the  drawing  is  correct 
as  to  its  dimensions  and  shape.  The  word  projection  is 
derived  from  two  Latin  words,  pro,  forth,  and  jacio, 
to  throw ;  so  that  the  literal  meaning  of  "  orthographic 
projection  "  is  a  correct  view  thrown  from  the  object  upon 
a  plane  surface. 

It  must  also  be  understood  that  the  "  projectors " 
thrown  forth  are  at  right  angles  or  perpendicular  to  the 
plane  of  projection — -that  is  to  say,  the  surface  upon  which 
the  drawing  is  made.  If  otherwise,  the  resulting  drawing 
might  be  a  "  projection,"  but  it  would  not  be  an  ortho- 
graphic projection. 

To  understand  this  clearly,  refer  to  Fig.  i,  page  47.  This 
is  a  sketch  of  a  triangular  block  of  wood  suspended  in  the 
air  for  a  purpose  that  will  presently  be  seen,  and  arranged 
with  its  several  edges  parallel  to  three  planes  which  are 
mutually  perpendicular  to  each  other.  The  planes  are 
further  shown  in  dotted  lines  unfolded  into  one  plane, 


THEORY    OF    ORTHOGRAPHIC    PROJECTION     49 

but  for  the  moment  we  will  confine  our  attention  to  those 
marked  a-b,  c-d&nde. 

a-b  is  the  vertical  plane,  and  c-d  the  horizontal  plane  ;  e  is 
a  special  or  auxiliary  vertical  plane  perpendicular  to  the 
other  two,  which  are  known  as  co-ordinate  planes.  Now, 
if  we  stand  exactly  in  front  of  the  prism,  looking  in  the 
direction  of  the  arrow  H,  we  shall  see  the  side  marked 
i,  2,  3,  4,  but  though  we  know  that  it  is  inclined,  having 
the  solid  before  us,  we  cannot  see  the  inclination  in  this 
position.  What  we  do  see  is  the  exact  height  measured 
perpendicularly  between  the  upper  and  lower  edges,  also 
the  exact  length  between  the  ends,  and  to  obtain  this  view 
upon  the  plane,  projectors  marked  p  are  imagined  to  shoot 
forth  from  each  extremity  of  an  edge  until  they  intersect 
the  plane.  If  these  points  are  joined  by  straight  lines,  as 
at  A,  an  "  elevation"  of  the  object  is  obtained  upon  the 
vertical  plane.  In  like  manner,  imagine  other  projectors 
shooting  forth  from  the  base  until  they  impinge  upon  the 
horizontal  plane  ;  their  points,  joined  up  as  at  P,  produce 
the  "  plan,"  or  view,  we  should  see  if  looking  straight 
down  from  above  the  object.  With  these  two  views  we 
can  obtain  the  correct  height  and  length  of  the  prism,  but 
not  the  real  length  of  its  inclined  sides ;  to  obtain  these  we 
must  use  the  auxiliary  plane  which  is  arranged  parallel 
with  the  end  of  the  prism.  Three  projectors  shot  forth 
on  to  this  plane  as  shown  will  give  the  shape  of  the  end. 
This  view,  E,  is  termed  an  end  elevation.  If  now  we  unfold 
the  planes  into  one  surface,  as  indicated  by  the  dotted  lines, 
we  get  the  three  views  in  their  relative  positions  above  and 
below  the  ground  line  G-L.  Fig.  2  shows  the  complete 
plane  with  the  views  or  projections  in  correct  position,  as 
they  appear  upon  a  sheet  of  drawing  paper,  and  it  will  be 
clear  that  not  only  can  we  obtain  all  the  dimensions  from 
these  three  views,  but  also  the  height  of  the  object  above  the 
ground  (shown  at  A)  and  its  distance  from  the  vertical 
plane  (shown  at  E  or  P).  It  should  be  noted  that  only 
what  is  visible  upon  the  surface  of  the  object  we  are  looking 
D 


50  PROJECTION    OF    A    CUPBOARD 

at  is  projected  or  shown  upon  the  plane  behind  it.  We  do 
not  attempt  to  depict  anything  that  is  upon  the  rear  surface. 
If  this  is  required,  auxiliary  planes  are  assumed  upon  which 
the  required  view  is  projected,  though  we  can,  of  course,  dot 
upon  any  view  details  which  are  hidden  from  the  eye. 

Having  now  explained  the  theory  of  orthographic  pro- 
jection, we  will  consider  the  examples  given  in  detail. 

A  Dwarf  Cupboard,  page  51. — The  size  of  this  cup- 
board is  to  be  3  ft.  4  in.  long,  i  ft.  8  in.  wide  and  3  ft.  in 
height.  The  ends,  top  and  shelf  are  to  be  i  in.  thick, 
the  framed  doors  ij  in.  thick  with  3^  in.  hanging  stiles, 
4  in.  meeting  stiles,  3  in.  top  rails  and  4  in.  bottom  rails. 
The  bottom  rail  of  front  is  ij  in.  x  ij  in.,  the  back  rail 
2j  in.  x  f  in.,  and  the  match-lined  back  5 J  in.  x  f  in. 

We  have  now  all  the  necessary  dimensions,  and  proceed 
to  lay  down  the  block  plan,  Fig.  i.  In  the  same  relative 
position  on  your  paper  as  it  is  shown  in  the  copy,  draw  in 
with  the  T-square  and  set  square,  to  any  convenient  scale, 
a  rectangle  3  ft.  4  in.  x  i  ft.  8  in.,  and  a  similar  rectangle, 
Fig.  2,  to  represent  the  end  elevation  3  ft.  x  i  ft.  8  in. 
You  will  note  that  there  is  little  to  distinguish  these  but 
their  position.  You  have  just  seen  that  plans  are  drawn 
upon,  or  parallel  with,  the  ground  ;  and  elevations  at 
right  angles  or  perpendicular  to  the  same.  Now  on  our 
sheet  of  paper,  the  line  marked  G-L  marks  the  lower  limit 
of  ground  line  for  the  elevations,  and  all  drawings  made 
above  it  are  in  elevation,  and  all  below  it  in  plan. 

We  next  proceed  to  lay  down  the  details  of  the  cupboard 
showing  its  construction,  Fig.  3.  Draw  the  lines  a-b  and 
d-c,  with  the  T-square,  projecting  them  from  the  block 
plan  as  shown  by  the  dotted  lines  ;  these  dotted  lines  are 
known  as  "  projectors,"  and  though  printed  in  the  copy, 
will  be  in  pencil  only,  upon  your  drawing,  to  be  rubbed  out 
later  when  the  inking-in  process  is  over.  Mark  off  along 
a-b  3  ft.  4  in.  to  scale,  and  draw  the  perpendiculars  a-d, 
b-c.  You  will  now  have  an  outline  on  your  paper  exactly 
as  Fig.  i,  and  in  future  work  this  is  all  that  will  be  necessary, 


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52  METHOD    OF    DRAWING 

Fig.  i  being  superfluous.  Next  scale  off  the  thickness  of 
the  doors,  ends  and  back  as  given  in  the  specifications,  and 
draw  in  parallel  lines  representing  the  insides  ;  then  set  off 
the  stiles.  To  obtain  position  of  meeting  stiles,  set  off  a 
centre  line  in  the  width.  This  will  be  I  ft.  8  in.  from  either 
end,  the  bead  is  \  in.  wide,  so  set  off  J  in.  on  each  side  of 
centre  line,  then  3|  in.  each  side,  which  will  be  the  inner 
edges  of  the  stiles.  Next  set  off  \  in.  within  these  edges  for 
plough  grooves  and  mark  across.  Draw  the  panels  in  the 
middle  of  the  thickness  f  in.  thick.  Draw  a  J  in.  rebate 
in  the  ends  to  receive  the  back  and  divide  up  the  width  into 
5 1  in.  boards.  Indicate  the  tongues  by  short  lines.  This 
completes  what  is  generally  termed  the  "  plan/'  but  which  is 
really  a  horizontal  section  which  we  may  assume  is  taken 
on  the  line  B-B,  Fig.  4 — That  is,  if  the  cupboard  existed, 
and  it  were  cut  through  with  a  saw  upon  the  line  B-B, 
the  appearance  at  the  line  of  cut  would  be  as  shown  in  Fig. 
3.  We  can  next  project  the  front  elevation  (Fig.  4)  from 
the  plan.  The  dotted  lines  indicate  the  direction  of  these 
and  they  will  obviously  be  made  with  the  set  square  resting 
upon  the  T-square,  which  is  held  with  its  top  edge  just  clear 
of  the  line  a-b. 

The  lines  are  stopped  at  a  horizontal  projector  drawn  from 
the  top  of  Fig.  2  as  shown.  This,  of  course,  locates  the  top 
of  the  cupboard.  After  drawing  the  outline,  we  may  scale 
off  the  dimensions  of  the  various  parts  as  given  in  the 
specification  at  the  commencement,  or,  as  is  more  usual  in 
practice,  proceed  at  once  with  the  vertical  section  (Fig.  5) 
in  a  similar  manner  to  that  prescribed  for  the  horizontal 
section,  and,  having  obtained  the  width  and  thickness  of  the 
various  parts,  we  then  project  them  into  the  elevation,  the 
intersection  of  the  two  sets  of  projectors  completing  the 
elevation  mechanically. 

The  above  procedure,  with  trifling  variations,  will  answer 
for  the  reproduction  of  the  following  examples,  and  if  the 
student  is  not  clear  as  to  the  actual  construction  of  the  fitting 
he  is  referred  to  page  95,  where  an  isometric  view  of  the 


54  A   FIELD   GATE 

complete  cupboard  is  given.  It  may  be  pointed  out  that 
the  two  sections,  Figs.  3  and  5,  if  drawn  full  size,  would  con- 
stitute a  "  rod  "  or  working  drawing,  all  that  would  be  neces- 
sary for  a  joiner  to  "  set-out  "  the  cupboard  by. 

It  must  also  be  explained  that  although  for  convenience 
of  reference  the  examples  are  to  some  extent  arranged  in 
order  of  trades  they  are  not  constructively  grouped,  as  in 
the  author's  works  on  Practical  Carpentry  and  Joinery. 
Here  they  are  placed  in  accord  with  their  comparative  diffi- 
culty of  drawing,  and  a  few  constructional  notes  are  added 
to  explain  the  purpose  or  uses  of  the  objects  represented. 

A  Field  Gate. — Not  much  difficulty  will  be  met  with  in 
reproducing  this  drawing  with  the  copy  as  a  guide,  but  with- 
out it  the  varying  thicknesses  of  the  bars  (introduced  with  a 
view  to  reduce  the  strain  upon  the  heel  post  and  the  hinges) 
offer  some  difficulty  to  a  beginner. 

Lay  down  the  plan  first,  commencing  with  the  posts  ; 
leave  the  hinges  until  last.  Next  draw  in  the  sections,  and, 
projecting  from  these,  the  elevation  is  readily  obtained. 
Take  note  that  the  top  bar  only,  which  is  thicker  than  the 
others,  is  tenoned  through  the  stiles  ;  the  others  are  stub 
tenoned  and  drawbore  pinned,  the  mortises  are  made  taper- 
ing so  that  the  tenon  jams  tightly  as  it  comes  home.  The 
heel  post  is  made  thicker  than  the  rest  of  the  gate  as  all  the 
strain  is  thrown  upon  it  and  the  wide  bracket  is  formed  on 
it  to  stiffen  the  top  bar. 

This  particular  form  of  gate  is  chiefly  used  in  Gloucester- 
shire and  Wiltshire.  Fig.  4  is  a  section  close  to  striking 
stile ;  Fig.  5  a  side  elevation  of  the  hanging  post  with  the 
gate  thrown  right  back. 

Types  of  Roofs,  page  55. — These  are  illustrations  of 
the  various  kinds  of  roofs  used  in  buildings  of  comparatively 
small  span. 

The  Couple  Roof,  Fig.  I,  is  the  simplest  construction, 
consisting  of  pairs  of  common  rafters  spaced  about  a  foot 
apart,  resting  upon  timber  wall  plates  at  the  foot,  and 
abutting  upon  a  thin  ridge  board  at  the  head. 


56  ROOF    TYPES 

The  Couple  Close  Roof,  Fig.  2,  has  the  feet  of  the 
rafters  tied  together  by  nailing  the  ceiling  joists  to  them, 
which  strengthens  the  roof  considerably,  thus  enabling  it 
to  be  used  for  wider  spans  than  the  previous  form. 

The  Collar  Beam  Roof,  Fig.  3,  shows  the  tie  or  collar 
placed  higher  up  in  the  roof,  to  increase  the  space  in  the 
room  below.  When  this  type  of  roof  is  used  it  is  necessary 
to  have  heavier  common  rafters  than  in  the  preceding  types. 

The  Collar  Bolt  and  Tie  Roof  (illustrated  in  the  same 
figure)  is  a  form  used  in  wider  spans,  where  the  ceiling 
joists  would  sag  in  the  middle  if  unsupported  ;  consequently 
a  light  bolt  is  attached  to  the  ridge  and  passes  through 
the  middle  of  the  joists.  Sometimes  a  plate  is  fixed  across 
the  top  of  the  joists  and  the  bolts  are  attached  to  this  about 
four  feet  apart. 

The  King  Post  Truss ,  Fig.  4,  consists  of  a  triangular 
frame  fastened  together  with  mortise  and  tenon  joints,  which 
are  secured  by  iron  straps  or  bolts,  as  shown  in  the  details. 
These  frames  or  trusses  are  spaced  about  8  to  10  ft.  apart, 
and  carry  the  ridge,  purlins  and  pole  plates  which  support 
the  common  rafters  and  the  covering.  They  also  support 
the  ceiling  joists,  which  are  either  spiked  to  them  or  framed 
into  the  lower  member  as  shown  in  Fig.  4. 

The  drawing  shows  two  half -trusses  of  different  pitches, 
the  one  suitable  for  tile  covering  and  the  other  for  slates 
(see  enlarged  detail,  Fig.  6).  All  of  these  drawings  are  in 
elevation,  and  can  be  drawn  directly,  from  the  examples. 
The  walls  should  be  drawn  in  first  at  the  required  distance 
apart,  then  the  wall  plates,  and  the  common  rafters  by  aid 
of  the  30°  set  square.  Usually  2  in.  of  "  back  "  is  allowed 
in  the  rafter  above  the  angle  of  wall  plate. 

Having  drawn  the  back  line,  scale  off  the  depth  of  rafter 
and  draw  the  under  side  parallel.  The  king  post  truss  will 
be  drawn  similarly,  commencing  with  walls  and  tie  beam. 
Then  find  the  middle  and  draw  in  a  centre  line,  about  which 
scale  off  the  king  post.  The  joints  should  be  copied  from 
the  enlarged  details.  One  side  of  the  drawing  shows  a 


A  Laminated  Rib  Roof 

Fig.   i.  Cross  Section.     Fig.  2.  Detail  at  foot  of  Rib.     Fig.  3.  Eleva- 
tion of  Fig.  2 


58  EMY    ROOFS 

parapet  finish,  the  other  an  eaves  finish.     Braces  should  be 
pitched  at  same  angle  as  the  rafters. 

The  Laminated  Rib  Roof  shown  in  Fig.  i,  page  57  is 
an  adaptation  of  Colonel  Emy's  system  of  laminated  ribs. 
The  details  are  somewhat  different  from  those  first  used  by 
the  inventor,  a  French  engineer  who  adopted  the  method 
of  forming  large  arched  ribs  by  means  of  thin  boards  bent 
around  a  drum  or  templet,  first  about  the  year  1820.  Emy 
used  this  form  of  roof  for  very  large  spans  up  to  60  ft.  and 
80  ft.  In  these  large  roofs  he  strengthened  the  arch  by 
adding  extra  boards  at  the  haunches — that  is,  to  points 
about  two-thirds  its  height  above  the  springings.  The 
design  shown  is  suitable  for  a  roof  of  moderate  span,  the 
trusses  being  spaced  about  8  ft.  apart. 

A  detail  to  enlarged  scale  is  given  in  Fig.  2,  which  will 
show  the  construction.  The  downward  thrust  of  the  arch 
is  taken  by  corbel  stones  resting  upon  piers,  and,  where  the 
walls  are  not  of  considerable  thickness,  piers  or  buttresses 
must  be  built  to  counteract  the  spread  of  the  ribs.  The 
arch  is  formed  of  six  ij  in.  boards,  6  in.  wide,  steamed  and 
bent  around  a  drum  ;  they  are  left  on  the  same  a  sufficient 
time,  to  take  a  considerable  "  set  "  or  curve.  Emy  fastened 
the  laminae  together  with  wood  pins,  and  though  nails  are 
often  used,  the  pins  would  undoubtedly  be  better.  Screws 
are  sometimes  used,  and  in  other  cases  the  laminae  are  bolted 
all  together.  In  the  present  case  the  boards  are  cut  back  at 
the  foot  of  the  rib  and  fitted  into  notches  in  the  wall  post. 
A  front  view  of  these  notches  is  given  in  Fig.  3,  which  is 
an  elevation  of  the  lower  end  of  truss,  with  the  rib  removed. 
The  rib  is  bolted  to  the  truss,  which  is  of  the  collar  beam 
type,  at  three  points.  The  wall  post  is  framed  into  the  foot 
of  the  principal  rafter  to  resist  the  spreading  of  the  latter, 
which  is  also  counteracted  by  the  heavy  wall  plate  built 
into  the  wall,  and  on  which  sits  the  pole  plate  carrying  the 
feet  of  the  common  rafters.  These  are  shown  sailing  over 
the  eaves,  but  the  finish  of  these  is  immaterial ;  they  might 
equally  well  finish  behind  a  parapet. 


DOORS  59 

The  collar  beam  will,  unless  the  roof  settles  or  spreads,  be 
in  compression  ;  but,  as  the  latter  contingency  may  possibly 
occur,  it  will  be  better  to  provide  for  its  becoming  a  tie  beam 
by  tenoning  it  to  the  principal  rafters  and  securing  these 
with  pins  or  iron  straps. 

Not  much  difficulty  will  be  experienced  in  making  this 
drawing.  Set  off  the  walls  to  the  given  span,  bisect  the  span 
and  erect  a  centre  line.  Draw  the  corbels  resting  on  the 
springing  line,  and  with  a  radius  of  19  ft.  describe  the  soffit 
of  the  arch  and  the  back  9  in.  farther  out.  Next  draw  in 
the  collar  beam  tangent  at  the  crown,  and  the  two  principal 
rafters  at  a  pitch  of  45°  tangent  to  the  arch  ;  the  remaining 
lines  are  parallel  to  these  and  can  easily  be  followed  from 
the  example.  It  is  a  good  method  in  all  drawings  to  get  in 
the  most  important  or  essential  member  first,  constructing 
those  of  less  importance  around  it  as  circumstances  suggest. 

Doors. — The  framed,  ledged  and  braced  door  in  solid 
frame  shown  in  Figs.  I  to  3,  page  59  is  a  strong  door  of 
the  ledge  and  batten  type  used  for  coachhouses,  warehouses, 
etc. 

The  stiles  and  top-rail  are  of  equal  thickness,  in  this  case 
2  in.,  and  are  grooved  to  receive  the  boards.  The  middle 
and  bottom  rails,  termed  "  ledges,"  are  usually  half  the 
thickness  of  the  framing,  the  remaining  half  being  occupied 
by  the  boards  or  "  battens  "  ;  these  are  grooved  and  tongued 
together  with  straight  tongues,  the  two  outside  boards  being 
rebated  and  tongued  to  the  frame,  as  are  also  the  top  ends  of 
the  remainder.  The  boards  are  nailed  to  the  ledges  and 
braces  with  wrought  nails.  Braces  should  rake  downwards 
towards  the  hanging  stile  for  the  purpose  of  throwing  the 
weight  upon  the  hinges,  and  be  notched  into  the  ledges  as 
shown.  The  ends  should  not  be  taken  into  the  angles,  as 
this  has  a  tendency  to  push  the  shoulders  off.  Barefaced 
tenons  are  cut  on  the  ledges,  and  the  top  edges  of  the  latter 
"  weathered  "  to  carry  off  the  water.  These  doors  are 
usually  hung  with  hook  and  eye  straps.  The  frame  is  out 
of  4 J  in.  X  3  in.  deal,  solid  rebated  and  beaded ;  4  in. 


DOOR    SPECIFICATIONS  61 

horns  are  left  on  for  fixings  at  the  head  and  f  in.  iron  plugs 
driven  in  the  feet  of  the  jambs  for  fixing  in  the  stone  sill. 

Commence  with  the  plan,  drawing  the  stiles  of  the  door 
first  to  the  given  dimensions.  Construct  the  frame  around 
these,  drawing  the  sight  lines  first,  \  in.  within  the  edges  of 
the  door.  Divide  up  the  panel  equally ;  next  the  vertical 
section  at  a  convenient  distance  from  the  boundary  of  the 
elevation,  the  position  of  which  can  be  seen  in  the  plan. 
Here,  first  draw  in  height  and  thickness  of  door,  then  head 
of  frame,  the  detail  being  taken  from  the  enlarged  details 
shown  in  Fig.  7.  Set  off  the  middle  ledge  3  ft.  J  in.  above 
the  ground  and  its  width  8|  in.  down  ;  lift  the  bottom 
ledge  f  in.  clear  of  the  ground  and  weather  the  top  edges  J  in. 
Put  in  minor  details,  then  project  from  the  two  sections 
into  the  elevation,  starting  with  the  frame  and  finishing 
with  the  hinges. 

The  four-panel  door  (Figs.  4-6)  is  shown  with  alternative 
treatment  of  the  panels  :  on  the  left,  the  stile  is  removed  to 
show  the  method  of  forming  the  tenons,  and  plain  panels 
are  shown  ;  these  are  described  simply  as  "  square  panel  " 
or  "  square  both  sides/'  It  would  be  clearer  if  described  as 
"  square  and  sunk  "  ;  the  term  "  square  "  really  refers  to  the 
framing  which  is  not  moulded,  or  is  left  square,  the  panel 
is  rightly  described  as  sunk  to  distinguish  it  from  a  flush 
panel  with  which  the  framing  might  also  be  "  square." 

The  treatment  on  the  right  side  is  usually  described  as 
"  moulded  and  square,"  sometimes  as  "  moulded  one  side 
and  square  sunk."  Planted  (that  is,  stuck  separately  and 
nailed  in)  mouldings  are  always  understood,  unless  "  solid  " 
or  "  stuck  "  is  specified.  The  student  will  of  course  under- 
stand that  a  door  will  be  treated  throughout  in  one  or  other 
of  the  given  methods,  and  not  as  shown  with  two  methods 
in  one  door.  When  the  panels  are  moulded  on  both  sides, 
as  in  the  enlarged  detail  of  Fig.  4,  it  is  described  as  panelled, 
and  moulded  both  sides,  sometimes,  as  twice  moulded. 

The  instructions  for  drawing  the  other  door  on  the  same 
plate  will  serve  also  for  this  one.  In  drawing  the  mouldings 


A  Diminished  Stile  Sashed  Door  in  Solid  Frame 

Fig.    i.    Section.      Fig.    2.    Half  Plans.      Fig.    3.    Half  Elevations. 
Figs.  4  and  5.   Enlarged  Details 


FLOORS  63 

in  elevation  it  is  best  to  project  one  piece  of  moulding 
complete,  then  to  draw  in  the  four  mitres  with  the  45°  set 
square,  and  to  continue  the  lines  around  from  the  inter- 
section of  the  members  with  the  mitre  lines. 

The  Diminished  Stile  Sashed  Door  shown  on  page 
62  is  a  type  commonly  used  in  passages  to  cut  off  the 
service  apartments  from  the  dwelling-rooms,  in  which 
situation  it  is  oftener  hung  in  a  solid  frame  than  in  jamb 
linings,  and,  as  the  head  is  usually  cut  between,  instead  of 
built  into,  the  wall,  as  in  the  case  of  outside  frames  the 
tenons  are  shown  haunched  back. 

This  door  is  not  essentially  more  difficult  to  draw  than  the 
previous  examples,  if  care  is  exercised  in  projecting  the 
appropriate  details  to  the  side  dealt  with.  It  will  be  seen 
that  the  elevation  shows  on  one  side  the  back  view  and  upon 
the  other  the  front  view  of  the  door  and  frame.  The  plan 
likewise  shows  in  one  half  a  section,  above  the  middle  rail, 
and  the  other  a  section  below  the  middle  rail.  These  sections 
should  be  copied  from  the  enlarged  details,  referring  to  the 
small  scale  section  to  see  the  arrangement  of  the  parts. 

It  will  be  noticed  in  the  enlarged  detail  of  the  back  rail 
that  the  tenons  are  shown  in  full  line  ;  this  is  for  clearness. 
They  cannot,  of  course,  be  seen  on  this  section  and  should 
rightly  be  dotted  lines. 

Floors. — A  "  single  "  floor  suitable  for  a  small  house  of 
the  suburban  villa  type  is  shown  on  page  64,  and  will  be 
found  an  interesting  example  in  projection.  In  this  instance 
the  plan  should  be  drawn  first,  commencing  with  the  walls, 
which  are  one  brick  or  9  in.  thick ;  the  interior  division  walls 
are  four  and  a  half  brickwork  set  in  cement.  Place  the  wall 
joists  about  ij  ins.  clear  of  the  walls  and  space  out  the  rest 
equally.  The  bridging  joists  are  9  in.  x  2  Jin.  The  trimming 
joists  which  carry  the  trimmers  at  the  ends  of  the  openings 
are  half-an-inch  thicker  than  the  bridging  joists.  Note  the 
small  trimmer  at  the  head  of  the  staircase  ;  if  this  were  not 
used  the  trimming  joist  would  need  to  be  brought  forward 
and  so  cause  an  extra  bridger  to  be  used  throughout.  En- 


Ftg.2 

Sccde  of  Feat 
W 


=§* 


Fig.  4 


A  Single  Floor,  with  Details 

Fig.    i.    Plan    of    Naked    Floor.     Fig.   2.    Section    on 
Section  on  C-D.     Fig.  4.  Details  of  Breastsummer 


?.     Fig.    3. 


WINDOWS  65 

larged  details  of  the  breastsummer  carrying  the  floor  across 
the  bay  window  are  given  in  Fig.  4.  This  is  composed  of 
three  9  in.X3  m-  deals  bolted  together  and  stub  mortised 
to  receive  the  tusk  tenons  on  the  joists  as  shown.  The 
transverse  sections,  Figs.  2  and  3,  are  projected  from  the 
plan  on  the  given  section  lines. 

Windows. — A  cased  sash  frame  with  2  in.  double-hung 
ovolo  moulded  sashes  is  shown  on  page  66,  with  enlarged 
details  on  page  68.  Two  methods  of  construction  are 
given  on  page  66 :  the  left-hand  half -elevation  and  plan, 
also  the  vertical  section,  Fig.  2,  showing  the  method  em- 
ployed in  superior  work,  all  the  parts  being  grooved  and 
tongued  together.  A  framed  window  back  is  shown  below 
the  sill,  with  an  architrave  moulding  fixed  on  moulded 
grounds  and  plinth  blocks.  The  section  is  shown  broken 
for  want  of  space,  but  the  student  should  re-draw  it  in  full 
height  as  figured.  The  right-hand  half-plan  and  elevation 
show  the  construction  of  a  common  frame  simply  nailed 
together.  There  is  no  wood  window  back  in  this  case  ;  the 
wall  runs  straight  across  under  the  sill,  and  is  plastered, 
and  a  wide  window  board  is  used  on  which  the  architrave 
stops.  The  brick  reveals  on  each  side  show  successive 
courses. 

The  superior  frame  is  shown  fitted  with  a  ventilation 
piece  or  wide  bead,  tongued  to  the  sill ;  this  allows  the 
bottom  sash  to  be  opened  for  ventilation  between  the 
meeting  rails  without  causing  a  draught  at  the  bottom. 
In  common  frames,  the  usual  f  in.  or  f  in.  guard  bead  is 
made  J  in.  wider  than  the  side  ones,  and  is  bevelled  to  enable 
the  sash  to  clear  freely. 

In  drawing"  the  frame,  start  with  the  plan,  then 
the  section ;  the  sizes  of  the  opening  should  first  be  set 
off  from  page  66,  then  the  frame  "  built  in  "  from  the  en- 
larged details  given  on  page  68,  working  inwards  from  the 
brickwork.  The  chief  dimensions  are  :  linings,  4!  in.  x  i 
in. ;  sashes,  2  in. ;  pulley  stiles  and  head,  ij  in. ;  oak 
sill,  3  in.  (twice  weathered  and  throated  and  three  times 


A  Window  Frame  and  Finishings 

Fi?    i    Half  inside  and  half  outside  Elevations.     Fig.  2.  Half  Plans 
showing  alternative  Treatment.     Fig.  3.  Broken  Vertical  Section 


FRENCH    CASEMENTS  67 

grooved)  ;  parting  beads,  fin. ;  guard  beads,  f  in. ;  meeting 
rails,  i  J  in.  thick  ;  bevel  rebated  pocket  pieces,  if  in.  wide  ; 
sashes  ovolo  moulded,  J  in.  x  J  in. 

Note  that  the  groove  in  sill  for  iron  water  bar  is  in  line 
with  outside  lining  (this  is  often  wrongly  shown  in  books 
in  the  middle  of  the  sill,  where  it  would  do  more  harm  than 
good),  and  that  the  joint  between  the  plaster  and  the  grounds 
must  be  covered  about  f  in.  by  the  architrave,  also  that  the 
grounds  should  not  be  bevelled  more  than  J  in.,  otherwise 
they  cannot  be  "cramped  up"  without  damage  to  the  edges. 

The  French  casement  sections  shown  in  Figs.  3-5, 
page  68,  illustrate  the  details  of  construction  of  this  class 
of  window,  the  frames  of  which  are  invariably  made  "  solid  " 
as  distinguished  from  the  built-up  or  "  cased  "  construction 
of  the  sash  window  frame  described  above. 

Fig.  3  is  a  vertical  section  (broken)  through  a  large  frame, 
with  the  casements  opening  into  the  room.  In  such  cases 
it  is  necessary  to  fix  a  "weather  board"  (W)  right  across  the 
outside  of  the  casements  to  throw  the  water  well  off  the  sill ; 
the  joint  at  the  meeting  stiles  requires  bevelling,  as  shown 
in  the  horizontal  section,  Fig.  4,  so  that  the  casement  may 
open  freely  ;  the  joint  is  made  tangent  to  the  circle  described 
by  the  sash  in  its  path.  The  ends  of  the  weather  board  are 
sometimes  sunk  J  in.  into  the  jamb  and  mullion,  so  that 
water  shall  not  enter  there. 

The  sill  in  this  frame  has  a  tongue  (A)  worked  in  the  solid, 
which  is  cemented  into  a  groove  in  the  stone  sill  for  the 
purpose  of  keeping  water  from  passing  between  them. 
The  transom  overhangs  the  jambs,  to  throw  the  water  well 
clear,  and  a  throating  sunk  beneath  intercepts  any  that  may 
run  in  under  the  edge.  The  fanlight  opens  inwards  and  is 
hung  to  the  transom. 

The  dotted  lines  on  the  casements  indicate  the  tenons 
which  are  double,  in  the  meeting  stiles,  to  clear  the  hook 
joint  shown  in  Fig.  4.  The  mullion,  on  the  side  towards  the 
central  opening,  has  a  J  in.  groove  sunk  in  the  rebate,  into 
which  a  cock-bead  on  the  casement  stile  fits.  This  renders 


SHOP    FITTINGS  69 

the  joint  watertight.  The  side  lights  are  shown  as  fixed  ; 
the  small  groove  is  a  precaution  to  check  any  water  that 
may  gain  access  through  the  shrinkage  of  the  mullion. 

An  outward-opening  casement  is  shown  in  Fig  6.  This 
frame  has  a  metal  water  bar,  in  addition  to  the  weathering 
and  throating  of  the  sill,  to  prevent  snow  drifting  in.  As 
French  casements  are  used  also  as  doorways  it  is  advisable 
to  have  metal  upon  the  sills  to  prevent  wear  of  the  parts. 
The  transom  in  this  case  is  made  flush  with  the  jambs,  and 
as  the  fanlight  is  hung  at  the  top,  the  bottom  opens  inwards, 
consequently  rain  is  liable  to  be  blown  in  at  the  joint  ;  this 
is  caught  in  a  large  groove  sunk  in  the  rebate  and  conveyed 
through  a  "  weep  pipe  "  to  the  throating  outside. 

The  head  of  this  frame  is  rebated  in  the  same  way  that 
Fig.  3  is,  but  is  moulded  to  match  the  transom,  and  in  both 
cases  the  jambs  would  be  of  the  same  section  as  the  heads. 

Shop  Fittings  (a  draper's  counter,  page  70). — This 
example  will  be  found  much  easier  to  draw  than  to  con- 
struct, and  a  brief  description  of  the  parts  will  be  necessary 
to  the  understanding  of  the  drawings.  These  are  necessarily 
grouped  for  convenience  to  suit  the  size  of  the  page,  and 
should  be  redrawn  with  more  freedom  of  space.  The  plan, 
Fig.  i,  shows  the  general  arrangement ;  the  part  to  the  right 
of  the  line  A-A  is  a  section  through  the  drawer  compart- 
ments, and  to  the  left  of  the  line  the  parts  immediately  below 
the  top  are  shown.  It  will  be  seen  the  counter  has  a  narrow 
return  end  without  drawers,  and  with  a  door  and  lifting  flap 
between  it  and  the  main  counter.  The  general  disposition 
of  these  parts  is  more  graphically  shown  in  the  isometric 
drawing,  page  95.  Fig.  2  is  a  reverse  or  back  elevation  of 
the  main  counter,  showing  interior  fittings.  Fig.  3  is  a  front 
elevation  of  the  return  end,  but,  apart  from  the  doorway, 
applies  equally  to  the  main  counter.  Fig.  4  is  an  enlarged 
vertical  section — broken  to  avoid  reducing  the  scale  of  the 
parts,  all  the  parts  not  entirely  shown  being  repeats  of  what 
is  shown — on  A-A ,  showing  the  method  of  fitting  the  drawers 
to  the  case,  and  the  fixing  of  the  top  by  buttons,  which 


PAVILION    ROOF  71 

allows  it  to  swell  and  shrink  without  splitting  (see  also  page 
95  for  details).  Fig.  5  is  a  section  of  the  return  counter,  and 
its  use  is  to  obtain  heights  for  the  elevation.  Fig.  6  is  an 
enlarged  detail  of  the  drawer  blocks  and  runners.  Fig.  7 
is  an  enlarged  detail  through  the  door,  etc. 

Lay  down  the  plan  in  outline  first,  according  to  the 
figured  dimensions,  then  reproduce  Fig.  4  unbroken  to  given 
dimensions.  Work  this  with  care,  because  all  the  parts  in 
the  smaller  scale  drawing  will  be  taken  from  it.  No  par- 
ticular order  need  be  taken  in  making  such  a  drawing,  other 
than  to  observe  the  general  rule  to  get  in  the  outline  first, 
then  the  main  features,  leaving  small  details  until  the  last, 
so  that  in  case  of  any  error  in  the  main  dimensions  less  time 
will  have  to  be  lost  when  making  corrections.  Also  re- 
member that  in  technical  drawing  it  is  the  important  things 
that  count,  not  feeble  fidelity  to  truth  ;  for  instance,  to 
make  my  meaning  clear,  it  is  important  to  draw  the  handles 
of  the  drawers  exactly  where  they  are  wanted,  but  it  is  not 
important  to  show  their  detail  of  moulding,  or  even  their 
exact  size  ;  in  practice,  the  specification  will  sufficiently 
indicate  this  to  the  constructor.  See  also  remarks  on  the 
same  subject  in  Chapter  IX.,  "  Workshop  Drawings." 

The  Octagonal  Ogee  Roof  shown  on  page  72  is 
suitable  for  a  turret  or  a  pavilion  roof.  We  will  assume  that 
the  given  data  are,  that  the  side  of  the  octagon  is  to  be 
3  ft.  4  in.  and  the  span  8  ft.  3  in. ;  height,  8  ft.  from  under- 
side of  curb  to  top  of  ribs ;  the  curb,  6  in.  x  4  in. ;  hips, 
2  in. ;  ribs  ij  in. ;  purlins,  ij  in. 

Proceed  to  draw  the  plan.  At  any  convenient  place,  draw 
the  line  A  -B  and  set  off  on  it  the  given  span  as  at  a-b ;  at  these 
points  draw  lines  perpendicular  to  A  -B  on  each  side.  Make 
these  lines  equal  to  the  length  given  for  the  side — 3  ft.  4  in. 
as  at  X-X' ',  then  bisect  a-b,  and  from  the  centre  describe 
a  circle  passing  through  the  points  X-X'.  This  circle  will 
contain  the  ends  of  all  the  hips.  Around  its  circumference 
set  off  eight  divisions,  equal  in  length  the  given  side,  and 
join  up  these  points,  which  will  give  the  outline  of  the  curb  ; 


An  Ogee  Pavilion  Roof 

Fig.   i.  Sectional  Elevation.     Fig.  2.  Plan.     Fig.  3.  Joints  at    Finial. 
Figs.  4  and  5.   Joints  at  Foot  of  Ribs 


OBTAINING    SHAPE    OF    HIPS  73 

draw  in  the  inside  edges  parallel.  Draw  diagonal  lines  joining 
the  opposite  eight  angles,  and  on  each  side  of  these  draw  in 
half  the  thickness  of  the  hips.  The  octagonal  finial  is  7  in.  in 
diameter.  The  purlins  are  drawn  parallel  with  the  curb  sides, 
and  at  such  a  distance  from  the  finial  that  the  greatest  dis- 
tance between  the  hips  above  the  purlin  will  not  exceed  one 
foot,  otherwise  excessively  thick  boarding  will  be  necessary 
for  covering.  The  covering  boards  in  this  case  will  run 
horizontally.  At  the  middle  of  each  bay  draw  in  an  inter- 
mediate rib,  as  shown  in  Fig.  2. 

The  elevation,  Fig.  i,  is  also  shown  as  a  section  of  the 
roof  on  the  line  A-B,  which  is  usually  placed  parallel 
with  the  principal  front  of  the  building. 

Before  completing  the  section  we  will  consider  the  method 
of  deducing  the  shape  of  the  hip  or  angle  rib  from  the  given 
section,  as  shown  on  the  right-hand  halves  of  Figs.  I  and  2. 

To  obtain  Mould  for  Shape  of  Hips.— Draw  the 
approved  outline  of  roof  by  describing  curves  of  contrary 
flexure  as  shown  ;  the  given  radius  is  5  ft.  3 J  in.  and  the 
centres  are  upon  levels  taken  at  the  top  of  curve  and  top  of 
ribs — in  other  words,  at  the  springings.  Take  any  number 
of  points  in  the  curve,  as  i,  2,  3,  4,  5,  6,  and  drop  projectors 
from  them  into  the  plan,  cutting  either  of  the  hips  (centre 
line)  in  points  i',  2',  3',  4',  5',  6'.  Upon  these  points  erect 
perpendiculars  to  the  plan  of  the  hip,  and  make  them  equal 
in  height  to  the  same  numbered  ordinates  in  Fig.  I,  measur- 
ing the  latter  from  the  top  side  of  curb.  Having  obtained  the 
points,  i",  2",  3",  4",  5",  6",  draw  the  curve  through  them. 
This  mould  will  give  the  shape  to  cut  the  hips  out  to,  also 
the  line  of  "  backing,"  if  moved  inward  horizontally  on  the 
curb,  until  its  edge  coincides  with  the  side  of  the  hip  as  shown 
in  the  plan.  This  will  be  better  understood  by  referring  to 
the  elevation,  where  the  hip  just  in  front  of  A  is  shown  in 
elevation,  with  the  backing  of  one  side,  the  other  side 
being,  of  course,  invisible. 

To  draw  the  Elevation.— -Having  produced  the  outline 
as  described  previously,  divide  it  into  a  number  of  parts  as 


74  LANTERN    LIGHTS 

at  70,  8a,  ga,  loa,  na,  120. ;  from  these  points  draw  hori- 
zontal projectors  across  the  elevation — in  the  example, 
only  one-half  is  shown — also  drop  projectors  from  the  same 
points  into  the  plan  cutting  the  line  A-B,  as  shown,  in  points 
7,  8,  9, 10,  n,  12  ;  this  locates  the  position  of  the  numbered 
points  in  the  plan,  and  as  the  surface  of  each  bay  on  a  line 
parallel  with  its  curb  is  straight  across  from  hip  to  hip,  it 
will  be  obvious  that  if  the  pointsi,  2,  etc.,  are  projected  to  the 
next  hip  in  planes  parallel  to  the  curb  they  will  locate  similar 
points  upon  that  hip.  Having  done  so,  reproject  them  into 
the  elevation  to  meet  the  corresponding  numbered  hori- 
zontal projectors,  and  the  intersections  will  be  points  in 
the  curve  of  the  hip.  Again,  we  may  take  the  projectors  a 
step  farther,  to  an  intermediate  rib,  and  in  like  manner  obtain 
its  projection  ;  the  method  of  locating  the  points  will  be 
clear  by  following  the  numbers,  and  the  curves  can  be  drawn 
through  the  points  so  obtained.  Fig.  3  is  an  enlarged  detail 
of  the  joints  in  the  finial ;  Figs.  4  and  5  a  side  elevation 
and  plan  of  the  joints  at  foot  of  hip  and  angle  of  curb. 

Lantern  Lights. — Lanterns  are  lights  in  a  roof  ;  they 
differ  from  the  simpler  form  of  skylight  in  that  they  have 
not  only  top  lights  but  also  side  lights  more  or  less  vertically 
arranged.  A  lantern  consists  of  a  rectangular  or  polygonal 
frame  composed  of  sills,  heads  and  corner  posts,  with  some- 
times intermediate  mullions  ;  these  openings  are  fitted  with 
sashes  sometimes  fixed  and  sometimes  hung,  either  by  hinges 
to  the  top  or  centre  pivots  at  the  sides.  The  roof  is  some- 
times covered  with  slates  or  lead,  but  is  usually  glazed  also, 
with  either  movable  or  fixed  lights,  fitting  into  hip  and  cross 
rafters.  The  lantern  itself  is  usually  raised  from  the  roof 
upon  a  rough  curb  or  frame  of  timber,  covered  with  lead 
outside  and  having  panelled  framing  inside.  There  are 
great  varieties  of  detail,  several  of  which  are  shown  in  the 
author's  "  Modern  Practical  Joinery."  The  illustration 
accompanying  this  lesson  is  designed  to  meet  the  require- 
ments of  the  following  examination  question,  and  is  selected 
as  indicating  several  difficulties  in  construction :— 


76  DETAILS    OF    LANTERN 

"  Draw  the  plan,  elevation  and  section  of  a  lantern  light, 
measuring  6  ft.  x  8  ft.,  to  be  at  the  ridge  of  the  roof  of  a 
billiard-room.  To  have  upright  sides  glazed  and  partly  to 
open,  the  roof  glazed  but  not  to  open.  The  lantern  to  be 
ornamental." 

It  is  unusual  to  have  a  ridge  roof  to  a  billiard-room,  these 
rooms  being  generally  on  ground  or  first  floors  having  flat 
roofs.  Light  is  required  all  round,  which  complicates  the 
treatment. 

The  sketch  diagram,  Fig.  8,  indicates  how  the  roof  is 
hipped  back  for  the  purpose  of  obtaining  sufficient  room  to 
open  the  end  lights.  Lights  hung  at  the  top  are  the  best  for 
billiard-rooms,  as  centre-hung  lights  may  allow  rain  to  be 
blown  in  on  the  table.  Fig.  I  is  a  half -plan  of  the  skylights, 
the  right-hand  light  being  omitted  to  show  the  hip  rafter, 
which  is  similar  in  detail  to  the  ridge  section,  Fig.  5,  a 
lamb's-tongue  moulding  being  worked  upon  its  under  edge. 
The  bars  are  checked  into  the  bottom  rails,  as  shown  by  the 
dotted  lines  in  Fig.  7.  Fig.  2  is  a  half-horizontal  section 
through  the  lantern  itself,  and  details  of  the  corner  posts  and 
mullions  are  given  enlarged  in  Fig.  6.  Figs.  3  and  4  are  half- 
end  elevation  and  cross  section  respectively,  the  lower  part 
of  the  former  being  in  section  to  show  the  queen  post  truss 
necessary  to  carry  the  lantern.  The  interior  of  the  opening 
in  the  roof  is  lined  with  a  ij  in.  ogee  moulded  and  panelled 
framing.  Above  this  is  a  thick  moulding,  with  a  gutter 
formed  in  its  upper  side  to  receive  any  condensed  water  or 
to  catch  any  rain  that  might  drift  in  ;  this  escapes  through 
copper  pipes  at  each  end  of  the  sills,  as  shown  in  Fig.  4. 
The  lights  are  opened  by  means  of  rackwork  not  shown  in 
the  drawing.  The  oak  sills  are  mitred  and  bolted  together 
at  the  corners,  and  the  posts  are  stub  tenoned  to  them,  and 
secured  with  coach  screws.  Sheet  lead  is  dressed  up  the 
face  of  the  curb  and  an  apron  piece  is  turned  over  and  enters 
a  groove  in  the  under  side  of  sill.  The  curb  is  dovetailed 
and  spiked  at  the  angles.  The  roof  lights  may  be  fixed  with 
an  inserted  tongue,  as  in  Fig.  7,  or  a  solid  tongue  formed  on 


DOUBLE    CURVATURE    WORK  77 

the  head,  as  at  B,  Fig.  4.  The  stiles  of  the  top  lights  are 
grooved  for  the  glass,  not  rebated.  The  dotted  lines  in 
Fig.  8  indicate  position  of  trusses,  the  outer  four  being  king 
post  trusses. 

Circle-on-Circle  Entrance  Doors  and  Frame. — This 
is  an  example  of  projection  that  will  require  careful  and 
painstaking  work  on  the  part  of  the  student  if  he  is  to 
succeed.  The  author  is  not  aware  that  this  particular  form 
of  circle-on-circle  work  has  hitherto  been  dealt  with  in  books, 
though  doubtless  now  it  will  become  common  enough.  It 
is  perhaps  also  the  reason  that  architects  rarely  design  door 
frames  in  this  manner,  as  it  is  difficult  to  get  the  work 
properly  done.  This  is  not  the  place  to  enter  into  the 
practical  details  of  construction,  the  remarks  here  being 
confined  to  the  methods  of  producing  the  drawings  and 
obtaining  the  moulds.  There  is  a  full  description  in 
"  Modern  Practical  Joinery  "  of  how  these  frames  are  to  be 
constructed  when  based  upon  the  solid  known  as  thecuneoid, 
and  generally  those  instructions  would  apply  equally  to  the 
frame,  etc.,  now  to  be  described.  The  head  of  this  frame, 
also  of  the  soffit  lining  and  the  architrave,  is  based  upon  the 
cone,  as  indicated  in  the  small  sketch,  Fig.  7 — that  is,  the 
edge  of  the  frame  and  face  of  the  lining  radiate  equally  at 
the  crown  and  springings. 

The  plan  should  be  first  drawn  ;  and  should  not  present 
much  difficulty  at  this  stage  ;  a  centre  line  should  be  drawn 
and  produced  into  the  elevation,  and  the  centre  of  the  plan 
curves  located  upon  it,  by  producing  the  splayed  reveals 
until  they  intersect  at  A'.  This  forms  the  apex  of  a  cone 
(or,  to  be  exact,  a  semi-cone),  in  which  the  surface  of  the 
parts  composing  the  head  lie,  and  becomes  the  common 
centre  for  describing  the  various  curves  in  the  plan.  Having 
finished  the  plan  so  far  as  the  members  of  the  frame,  etc., 
are  concerned,  the  elevation  may  be  projected  therefrom. 

The  opening  in  the  wall  should  first  be  drawn,  and  it 
should  be  noted  that,  although  the  head  is  shown  as  a  semi- 
circle on  the  flat,  it  is  not  so  actually,  the  true  contour  being 


78  PROJECTING    CURVED    SECTIONS 

elliptic.  What  is  actually  drawn  in  the  elevation  is  a  pro- 
jection upon  a  plane  standing  on  the  line  B-B.  The  dotted 
projectors  indicate  where  the  various  lines  in  the  elevation 
are  obtained  from  in  the  plan,  and  no  difficulty  should  be 
experienced  in  tracing  these  ;  and  we  can  now  proceed  with 
the  sectional  elevation,  Fig.  3,  which  is  the  really  difficult 
part  of  this  example. 

To  obtain  the  Vertical  Section. — Draw  the  ground 
line,  mark  point  C',  and  project  it  to  the  head.  This  point 
represents  the  highest  point  of  the  reveal  in  the  brickwork, 
as  indicated  by  the  dotted  projector  c'-c" ;  intersect  this  by 
a  horizontal  projector  from  the  crown  of  the  arch  /  as  shown. 
Next  consider  that  the  section  we  are  drawing  is  a  view 
obtained  by  looking  in  the  direction  of  the  arrow  on  Fig.  i, 
at  a  plane  passing  through  the  line  C—A ' ;  if  then  we  draw 
projectors  perpendicular  to  C-A'  from  the  various  members 
and  transfer  these  to  the  ground  line  in  Fig.  4,  as  points 
i',  2',  3',  4',  5',  etc.,  the  location  of  the  various  edges  will  be 
obtained  for  projecting  into  elevation  up  to  the  springing 
line,  where  the  curves  commence  ;  and  we  next  have  to  plot 
points  in  these.  Let  us  take  the  sight  line  of  the  opening  as 
a  starting  point.  Divide  the  elevation  of  this  line  into  as 
many  parts  as  convenient,  as  at  a,  b,  e,  d,  /.  Draw  horizontal 
projectors  from  these  points  across  the  section,  also  drop 
projectors  from  them  into  the  plan,  cutting  the  line  of  the 
arch  therein  in  points  a',  br ,  e' ,  d',  /',  project  the  intersection 
points  to  C—A'  as  shown  by  the  chain  lines  ;  then  transfer 
them  to  the  ground  line  in  Fig.  3,  as  at  a",  V" ,  e"',  etc.,  and 
raise  perpendiculars  to  intersect  the  horizontals  from  the 
original  points  a,  b,  e,  etc.  These  intersections  give  the 
points  a2,  b2,  e2,  d2,  through  which  to  draw  the  curved  edge 
of  the  arch  soffit  in  sectional  elevation.  They  will  be  easily 
followed  by  inspecting  the  drawing.  The  arrises  of  the 
frame,  the  lining  and  the  architrave  are  obtained  in  like 
manner,  by  producing  the  projectors  in  the  plan,  to  cut  the 
desired  line,  then  projecting  these  points  to  the  line  of  section 
and  transferring  them  to  Fig.  4,  where  they  are  to  be  inter- 


Fiq.1. 


Circle-on-Circle  Entrs 


Fig 


Fig.   I.   Plans.     Fig.  2.  Outside  Elevation.     Fig.  3.    Inside   Elevation. 
ig.  6.  Method  of  obtaining  Face  Mould.     Fig.  7.  Constructional  Diagr; 


Fig.5. 


7    6    5 


Doors  and  Frame 

.   4.  Vertical  Section.      Fig.    5.    Method   of  obtaining   Soffit  Mould. 


To  come  betwttn  pp.  78-79. 


OBTAINING    SHAPE    OF    MOULDS  79 

sected  by  horizontal  projectors  drawn  from  the  corresponding 
points  in  the  elevation  ;  nearly  all  of  these  are  shown,  and, 
if  dealt  with  one  point  at  a  time,  following  each  through  its 
several  positions,  the  necessary  data  for  drawing  the  curves 
will  be  obtained  without  great  difficulty. 

It  will  be  seen  that,  to  avoid  a  confusing  mass  of  lines,  the 
same  projector  has  been  used  upon  several  arrises,  but  it 
must  be  noted  that  it  is  necessary  to  project  into  the  plan 
the  new  points  where  the  horizontal  projector  intersects 
the  arris  in  question,  and,  to  simplify  the  procedure,  it  is  best 
to  deal  with  one  arris  at  a  time  and  not  to  copy  off  all  the 
projectors  shown  on  the  plate  straight  away,  as  this  is  given 
in  its  completed  state,  with  all  the  construction  lines  upon  it. 
In  the  usual  way  many  of  these  lines  would  have  been 
removed  after  serving  their  purpose,  leaving  the  drawing 
clear  for  subsequent  projectors. 

To  obtain  the  Soffit  Mould,  Fig.  5. — This  figure  is 
drawn  to  half  the  scale  of  Fig.  I,  for  the  purpose  of  placing  it 
on  the  same  page,  but  in  the  reproduction  must  be  drawn 
to  the  same  scale  as  the  rest  of  the  drawing.  The  drawing 
shows  the  mould  for  the  soffit  of  the  frame,  but  the  method 
will  be  the  same  for  obtaining  that  of  the  lining  and  the 
architrave,  also  edge  of  the  ground. 

A—a-b  is  the  plan  of  the  cone  formed  by  the  radiating 
jambs  ;  the  semicircle  is  the  elevation  of  its  end  laid  down  or 
rebated  into  the  horizontal  plane.  Divide  the  semicircle  into 
a  number  of  equal  parts  as  shown,  project  these  points  to 
a-b,  then  carry  them  to  the  apex  A ,  as  shown  ;  next  describe 
the  development  of  the  edge  of  the  semi-cone.  With  A  as 
centre  and  A-a  as  radius,  describe  the  arc  a-12.  Make 
this  equal  in  length  to  the  semicircle  a-6-6  by  stepping 
around  same  with  the  compasses  and  transferring  a  like 
number  of  steps  to  the  development,  the  greater  the  number 
the  greater  the  accuracy  of  the  length  obtained.  Then 
transfer  in  a  similar  manner  the  numbered  points  i  to  n. 
Draw  lines  from  them  to  the  apex  A.  The  triangle  then 
obtained  will  be  the  shape  of  the  covering  or  "  envelope  " 


8o  OBTAINING    MOULDS 

of  the  semi-cone.  Next  describe  the  plan  of  the  frame 
(it  may  be  pointed  out  here  that  this  all  might  be  done 
upon  the  original  plan  ;  a  separate  drawing  is  used  only  to 
avoid  confusion  of  lines) ,  and  set  off  upon  the  development 
along  the  radiating  lines  points  at  a  like  distance  from 
the  edge  of  the  envelope  that  the  edges  of  the  frame  are,  in 
plan  from  the  line  a-b  as  measured  on  the  correspondingly 
numbered  radial  line,  and  so  obtain  a  series  of  points  through 
which  to  draw  the  mould.  For  example,  points  2-x-o  on 
the  development  are  made  equal  to  points  2-x-o  in  the  plan. 

To  obtain  the  Face  Mould  of  Frame,  Fig.  6. — Again 
draw  the  plan  of  frame  and  the  containing  cone.  Assuming 
the  head  to  be  made  in  two  pieces,  which  it  may  easily  be, 
draw  the  line  ~L-a,  joining  the  extremities  of  the  curve ; 
parallel  with  this  draw  a  second  line  tangent  to  the  curve. 
This  shows  thickness  of  stuff  required  to  get  the  head  out 
of.  Next  divide  the  line  i-a  into  a  number  of  parts,  as  a,  b, 
c,  d,'e.  Through  these  points  draw  perpendiculars  to  the 
centre  line  A-i,  cutting  the  side  of  the  cone  ;  with  the  points 
i,  2,  3,  4,  5  upon  the  centre  line  as  centres,  and  the  distance 
of  each  point  from  the  side  of  the  cone  as  radii,  describe 
arcs  as  shown  in  dotted  lines.  Intersect  these  by  projectors 
from  the  points  b,  c,  d,  i,  drawn  parallel  with  the  centre 
line  A-C,  thus  obtaining  points  i',  2',  3',  4',  5'.  Next 
erect  perpendiculars  to  i-a  from  points  i,  d,  c,  b,  a,  and 
make  them  equal  in  length  to  the  similarly  numbered  dotted 
ordinates  in  the  plan,  and  draw  the  curve  through  the  points 
so  found.  In  practice  the  back  edge  would  be  gauged 
parallel  from  the  front,  but  geometrically  it  may  be  obtained 
in  like  manner  to  the  soffit  edge  by  producing  the  projectors 
as  shown  at  2',  3",  4"  5". 

The  principle  upon  which  the  above  construction  is  based 
is  that  any  section  of  a  cone  passing  through  both  sides, 
as  shown  by  the  line  a-i  produced,  forms  an  ellipse  ;  also 
any  section  of  a  cone  parallel  with  its  end  or  perpendicular 
to  its  axis  is  a  circle  (in  the  case  of  a  semi-cone,  a  semi- 
circle). If  then  we  find  the  size  of  the  cone  at  various 


USE    OF    MOULDS  81 

points  where  a  perpendicular  plane  upon  the  line  i-a  would 
pass  through  it,  the  points  in  the  circumference  of  the  cone, 
as  indicated  by  the  projectors  i',  2',  3',  etc.,  will  also  be 
points  in  the  required  ellipse.  Only  one  mould  is  shown  ; 
another  is  required  for  the  outer  face,  but  the  procedure  is 
exactly  the  same,  the  superimposing  of  it  on  the  drawing 
would  only  confuse  the  reader. 

The  face  moulds  are  used  for  marking  the  elevation  curves, 
and  after  the  soffit  edge  is  planed  to  the  lines  the  soffit 
mould  is  applied  and  by  its  aid  the  plan  curves  are  drawn. 


CHAPTER  VI 
ISOMETRIC  PROJECTION 

Derivation  of  Term  Isometric.  Theory  of  Isometric  Projection 
— advantages  of  the  method.  To  construct  a  Parish's 
Scale.  A  Simple  Isometric  Scale.  Equal  Angle  Projection 
— its  principles.  Mechanical  Method  of  Construction.  The 
Isometric  Planes.  Examples — a  Nest  of  Shelves.  Mortise 
and  Tenon  Joint.  Non-rectangular  Figures.  Projecting  an 
Octagonal  Prism.  An  Octagonal  Pyramid.  A  Splayed  Washing 
Tray.  A  Gallows  Bracket.  A  Dwarf  Cupboard.  A  Brick  Quoin 
and  Footings — how  bricks  should  be  laid.  A  Builder's  Gantry — 
method  of  construction,  how  to  project.  A  Draper's  Counter — 
details  of  construction,  method  of  making  the  proj ection .  Circles 
and  Curves — how  they  may  be  rendered  in  isometric.  Pro- 
jecting a  Cylinder.  Isometric  View  of  a  Moulding 

ISOMETRIC  projection,  or  "projection  showingequal  measure- 
ments," as  it  was  described  by  the  inventor,  Professor 
Parish,  of  Cambridge  University,  derives  its  name  from  two 
Greek  words  ;  isos,  equal,  and  metron,  a  measure,  referring 
to  the  fundamental  principle  of  the  method  :  that  the  axial 
or  root  lines  of  the  drawing,  although  reduced,  are  equal 
in  length  or  measure,  and,  therefore,  proportionate  to  the 
object.  One  of  the  chief  advantages  of  this  method  of  draw- 
ing is  that  direct  measurements  may  be  taken  from  the 
isometric  axes  or  root  lines  of  the  drawing  just  as  in  ortho- 
graphic drawings.  A  further  advantage  is  that  three  views 
of  the  object  are  combined  in  one  drawing,  thus  giving  it 
an  appearance  of  solidity  that  is  very  convincing  ;  we  are, 
however,  practically  limited  to  one  position  only,  as  will  be 
better  understood  by  inspection  of  the  examples  than  by  a 
written  description. 

The  basis  of  isometric  projection  is  the  relative  positions 

82 


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84  ISOMETRIC    SCALES 

which  the  contiguous  sides  of  a  cube  assume  to  the  vertical 
plane,  when  it  is  resting  upon  one  of  its  corners  and  the 
diagonal  line  joining  the  corners  is  horizontal.  This  position 
is  shown  by  the  cube  drawn  in  Fig.  3,  page  83,  and  the 
lozenge  representing  the  upper  surface  of  the  cube  differs 
considerably  from  the  square,  which  is  its  actual  or  ortho- 
graphic projection,  as  shown  in  juxtaposition  in  dotted  lines. 
This  figure  will  explain  why  a  true  isometric  drawing  is 
smaller  than  the  object  it  represents,  apart  from  any  scale 
it  may  be  drawn  at.  If  the  square  c-a-b-d,  shown  in  dotted 
lines,  were  revolved  on  the  diagonal  c-b,  until  the  corner  a 
reached  point  a',  the  full-line  lozenge  c-a'-b-d'  would  be  its 
appearance  to  an  observer  immediately  in  front ;  it  would 
also  be,  as  we  shall  see  presently,  the  true  isometric  pro- 
jection of  the  square,  which  is  also  one  side  of  a  cube.  It 
will  be  obvious  that  although  the  position  of  the  sides  of 
the  square  are  altered  during  its  movement,  their  actual 
lengths  are  not ;  nevertheless  it  will  be  found  on  measuring 
the  projection  that  the  full  lines  are  shorter  than  the  dotted 
lines,  which  are  the  real  dimensions,  whilst  the  diagonal 
c-b  remains  the  same  throughout.  The  proportion  of  an 
isometric  line  to  the  real  line  it  represents  is  as  the  square 
root  of  2  is  to  the  square  root  of  3. 

An  isometric  scale  constructed  upon  the  above  principle 
for  the  purpose  of  making  an  isometric  projection  in  due 
proportion  to  a  given  scale  is  shown  in  Fig.  i. 

To  construct  an  Isometric  Scale. — Draw  two  lines, 
A -B  and  B-C,  perpendicular  to  each  other  and  equal  in 
length.  Join  A-C,  then  A-B  :  A-C  as  I  :  1/2.  Next 
make  A-D  equal  in  length  to  A-C,  and  D-E  parallel  to 
and  equal  in  height  to  B-C.  Join  A-E.  Then  A-E  is 
to  A-D  as  the  J/3  is  to  \J2.  We  have  now  two  lines 
in  the  desired  proportion  or  ratio  to  each  other,  and  if 
we  construct  a  common  or  regular  scale  upon  the  longer 
line,  A-E,  as  shown,  and  project  its  divisions  perpendicularly 
to  the  base  line  A-D,  the  said  divisions  will  be  proportion- 
ately reduced  thereon,  and  an  isometric  scale  constructed, 


THEORY    OF    ISOMETRIC    PROJECTION          85 

with  which  we  can  read  off  dimensions  in  the  same  manner 
that  dimensions  are  read  upon  an  ordinary  scale  in  ortho- 
graphic drawings.  The  above  is  Parish's  method,  but  the 
same  results  may  be  obtained  in  a  simpler  manner,  as  shown 
in  Fig.  2.  Here  two  lines  are  drawn  upon  the  base  line  A-D, 
having  angles  of  45°  and  30°  respectively  between  them. 
The  true  scale  is  plotted  upon  the  45°  angle  line  A-B,  and 
the  divisions  projected  as  before  upon  the  30°  line  A-C, 
which  becomes  the  reduced  or  isometric  scale.  This 
method  is  based  on  the  construction  shown  in  Fig.  3 .  Where 
the  dotted  line  C-a  is  at  an  angle  of  45°  with  the  horizontal 
diagonal  C-b,  and  the  full  line  c-a'  is  at  an  angle  of  30°  with 
the  horizontal,  and,  as  previously  explained,  the  full  line  is 
the  isometric  equivalent  for  the  real  edge  c-a,  it  follows  that 
any  portion  of  the  real  line  would  be  in  like  manner  repre- 
sented isometrically  by  dropping  a  perpendicular  from  it  to 
the  isometric  edge,  as  shown  at  /. 

It  is  advisable  to  be  acquainted  with  the  above  theory 
of  isometric  projection  for  a  full  understanding  of  the 
subject,  but  in  practice  it  is  usual  to  disregard  the  tact  that 
an  isometric  projection  is  smaller  than  the  object  repre- 
sented, whatever  scale  may  be  used,  and  to  mark  off  the 
required  dimensions  with  a  rule  or  an  ordinary  scale  upon 
the  three  root  lines  which  represent  respectively  the  length, 
breadth  and  thickness  of  the  object.  This  may  be  safely 
done,  as  every  part  of  the  drawing  is  proportionately 
reduced.  The  method  now  to  be  described  has  been 
variously  termed  pseudo-isometric,  conventional  isometric 
and  angular  projection.  Neither  term  is  entirely  distinc- 
tive or  very  illuminating,  and  the  writer  suggests  the  term 
equal  angle  projection  as  being  more  descriptive  of  the 
procedure. 

It  has  already  been  explained  upon  page  16  that  any 
circle  may  be  divided  into  360  equal  parts  for  the  purpose 
of  measuring  angles,  by  observing  how  many  degrees  or 
divisions  such  angle  contains,  and,  if  a  circle  is  divided  into 
three  equal  parts  by  lines  radiating  from  its  centre,  it  will  be 


86  MECHANICAL    PROJECTION 

obvious  that  each  of  these  lines  will  contain  120  degrees, 

- —  =  120.    This  construction  is  made  the  basis  of  the  form 

of  isometric  projection  now  to  be  described.  A  vertical  line 
is  drawn  from  the  centre  of  Fig.  4  to  the  circumference  a. 
Divide  the  circumference  into  three  equal  parts  from  point 
a,  as  at  B  and  C,  join  these  points  to  A,  and  we  have  the 
three  "  root  lines,"  or  isometric  axes,  upon  which  the  three 
cardinal  dimensions  can  be  measured  direct.  These  lines 
are  the  isometric  projections  of  the  edges  in  the  object  that 
are  perpendicular  to  each  other,  and  all  other  edges  or 
surfaces  that  are  parallel  to  these  edges  in  the  object  must 
be  made  parallel  to  these  axes  in  the  projection.  If  this 
requirement  is  observed,  no  mistakes  are  likely  to  be  made 
in  the  projection,  and  the  completion  of  the  cube  within 
the  circumscribing  circle  will  be  easy. 

Observe  that  upon  the  tangent  line,  a-c  is  marked  off  (to 
scale)  i  in.  long,  and  that  its  projector  is  a-c' ;  the  isometric 
projection  lies  in  this  line  also,  but  is  shorter,  falling  in  the 
circumference  of  the  circle,  but  it  measures  by  the  same 
scale  i  in.,  which  proves  that  although  isometric  projection 
shortens  the  edges  lying  in  the  isometric  planes,  it  does  not 
falsify  the  dimensions.  We  may  further  simplify  this  method 
of  projection  by  using  the  T-square  and  set  square,  as  shown 
in  Fig.  6,  to  produce  the  isometric  axes,  for  if  a  horizontal  line 
is  drawn  through  point  A  in  Fig.  4 — that  is,  perpendicular  to 
a- A — -the  angle  contained  between  such  horizontal  line  and 
either  A~B  or  A-C  will  be  30°  ;  therefore,  if  we  use  the 
set  square  of  30°,  as  shown  in  Fig.  6,  we  can  draw  A-B  and 
A—C  with  its  hypotenuse  edge  and  A— a  with  its  right-angled 
edge,  and  subsequently  any  parallel  line  or  edge  by  moving 
the  set  square  along  the  T-square  to  the  required  point. 
No  difficulty  should  be  experienced  in  drawing  the  remaining 
figures  upon  this  plate  if  it  be  remembered  that  all  dimen- 
sions are  to  be  marked  along  the  three  root  lines  and  projected 
parallel  therefrom.  Fig.  Q  represents  a  cube  resting  upon 
one  edge,  and  is  produced  by  revolving  the  circle  shown  in 


88  EXAMPLES    IN    PROJECTION 

No.  4,  with  its  points,  until  C-c'  lies  horizontal.  A  mortise 
is  shown  in  it  to  take  the  student  a  step  farther.  Fig.  10 
represents  the  theoretical  isometric  planes  with  prisms  lying 
in  them.  Any  plane  which  contains  two  isometric  axes  is 
called  an  isometric  plane.  Figs.  I,  2,  3,  page  87,  are 
rectangular  figures  that  will  not  offer  much  difficulty  to  the 
student. 

The  Nest  of  Shelves,  Fig.  i,  should  be  commenced  by 
drawing  the  root  lines,  a-a',  a-b,  a-c,  to  the  given  dimensions 
— preferably  not  less  than  three  times  the  scale  of  the  copy. 
When  these  are  drawn,  complete  the  outline  of  the  case  by 
drawing  parallels,  then  mark  off  the  thickness  of  the  sides 
equal  to  I  in.,  and  space  out  the  shelf  and  divisions. 
Fig.  2  is  an  enlarged  detail  of  one  side  and  end  of 
the  bottom,  showing  how  the  case  is  jointed  and  the 
shelf  housed  in. 

A  Corner  of  a  Frame  with  Mortise  and  Tenon  Joint 
is  shown  in  Fig.  3.  Probably  no  difficulty  will  be  met  with 
in  drawing  this  until  the  mortise  is  reached.  The  position 
of  this  must  be  located  upon  the  root  line  by  projecting  across 
the  inside  of  the  rail  to  a,  and  dropping  a  perpendicular. 
Mark  off  a  parallel  line  to  the  width  of  the  tenon  (as  shown, 
it  is  half  the  width  of  rail),  then  add  the  wedging  ;  finally 
draw  in  the  sides  of  the  mortise  and  project  them  to  the 
salient  angle  to  project  into  the  adjacent  plane,  and  so 
obtain  the  haunching.  Finish  by  indicating  the  tenon,  etc., 
by  dotted  lines  drawn  from  the  visible  faces. 

To  draw  Non- Rectangular  Figures  by  this  method 
it  is  first  requisite  to  enclose  them  within  a  rectangular  figure 
and,  placing  this  isometrically,  we  can  mark  off  the  points 
where  the  contained  figure  cuts  or  touches  the  sides  of  the 
rectangle,  just  as  we  should  dimension  points,  and,  joining 
up  these,  obtain  an  isometric  projection  of  the  figure.  Fig.  4 
is  an  Isometric  View  of  an  Octagonal  Prism,  and  the 
dotted  lines  indicate  the  containing  rectangle,  produced  as 
shown  in  Fig.  5.  It  will  be  observed  that  the  face  of  the 
prism  lying  below  the  line  b'—b"  is  shown  much  wider  than 


90  A    DWARF    CUPBOARD 

the  corresponding  face  below  c-c1 '.  This  is  a  defect  in- 
separable from  the  method. 

An  Octagonal  Pyramid  is  shown  isometrically  in 
Fig.  6.  To  produce  this  place  the  base,  Fig.  5,  in  the  hori- 
zontal isometric  plane  and  erect  a  perpendicular  from  the 
centre  X.  Locate  the  apex  upon  this  and  draw  lines  to  it 
from  the  angles  in  the  base. 

The  Washing  Tray,  Fig.  7,  has  four  equally  sloping 
sides,  therefore  is  non-rectangular  at  either  side.  To  draw 
it  the  dotted  rectangular  prism  must  be  made  upon  it  to  the 
required  size  of  top,  and  the  height.  Then  mark  off  the 
amount  of  slope  at  the  bottom,  as  at  a'-i,  a'-2,  £'-3,  etc., 
and  diaw  in  the  sides  to  the  intersections. 

The  Gallows  Bracket,  Fig.  8,  shown  in  orthographic 
projection  is  given  as  an  exercise.  The  student  should  put 
it  into  isometric  projection. 

The  Dwarf  Cupboard  shown  in  plan  and  elevation 
on  page  51  is  drawn  isometrically  on  page  89.  This  is 
distinctly  an  example  that  can  be  better  rendered  in  isometric 
than  in  orthographic  projection,  so  far  as  giving  a  clear 
impression  of  the  construction  is  concerned. 

It  is  an  easy  example  to  draw.  Commence  as  before  with 
the  three  root  lines,  making  these  represent  the  salient 
angle  of  the  case,  the  bottom  edges  of  the  front  and  end 
respectively.  Complete  the  case  by  drawing  parallels  to 
these,  taking  the  necessary  dimensions  from  page  51.  The 
doors  may  next  be  drawn,  commencing  with  the  closed  one  ; 
no  instructions  should  be  needed  to  locate  the  face  lines 
of  the  rails  and  stiles,  these,  of  course,  being  measured 
directly  upon  the  root  lines,  but  a  little  consideration  must 
be  given  as  to  what  parts  of  the  recessed  surfaces  will  be 
visible.  In  this  kind  of  drawing  the  observer  is  always 
supposed  to  be  standing  opposite  the  near  salient  angle, 
therefore  he  cannot  see  the  edges  which  face  away  from  him. 
Obviously  the  edge  of  the  hanging  stile  of  the  door  is  in  this 
position,  and  is  not  shown,  whilst  that  of  the  meeting  stile. 
is  ;  also  that  of  the  bottom  rail.  The  left-hand  door  is 


92  BRICKWORK    EXAMPLES 

projected  open,  and  as  at  this  stage  the  clear  opening  will 
be  shown,  commence  the  door  by  projecting  the  top  and 
bottom  edges  from  the  inner  angle  of  the  opening.  Eventu- 
ally the  lower  line  will  disappear,  being  hidden  by  the  back 
face,  but  it  is  necessary  to  first  draw  it  to  obtain  the  size 
of  the  door  and  the  thickness. 

Set  off  along  the  top  line,  the  width  as  shown  in  the 
opening,  and  draw  in  the  rebate,  projecting  the  back  edge 
J  in.  beyond  the  rebate  line  just  obtained.  Go  back  to 
point  A  and  set  off  the  thickness,  when  the  inner  face  may 
be  completed.  The  filling  in  of  the  minor  details  should 
offer  no  difficulty.  The  position  of  the  shelf  is  located  upon 
the  dotted  line  representing  the  inner  edge  of  the  case  as  at 
a,  projecting  back  the  thickness  of  the  door  to  find  the  plane 
of  the  edge  of  the  shelf. 

An  enlarged  detail  of  the  joint  between  the  end  and 
top  of  the  case  is  shown  in  Fig.  2.  The  bottom  rail 
is  stub  tenoned  into  the  ends  and  the  shelf  is  housed 
in  fV  in- 

The  Quoin  of  a  14  in.  Brick  Wall  in  single  Flemish 
Bond  is  shown  on  page  91,  with  three  courses  of  footings 
resting  on  the  surface  of  the  concrete  foundations.  The 
drawing  further  illustrates  the  technical  terms,  "  toothing," 
"  racking  back  "  and  "  carrying  up  the  quoin  "  ;  the  first 
being  the  method  of  connecting  to  a  cross  wall,  the  second 
the  method  of  suspending  the  work  in  successive  set-backs 
right  across  the  thickness,  for  the  purpose  of  bonding  the 
continuation  of  the  wall.  Some  difference  of  opinion  exists 
among  bricklayers  as  to  the  best  way  to  lay  the  bricks, 
frog  up  or  down,  but  undoubtedly  in  all  ordinary  cases  it  is 
better  workmanship  to  lay  with  the  frog  upwards,  as,  placed 
thus,  it  is  sure  to  get  filled  with  mortar.  The  bottom  course 
must  in  all  cases  have  the  frogs  uppermost,  and  the  top 
course  the  frogs  downwards. 

Carrying  up  the  quoin  is  the  building  up  to  the  two  ends 
of  a  wall  in  advance  of  the  remainder  for  the  purpose  of  lining 
the  courses  to  keep  them  level.  Quoin  is  the  corner  or 


94  PROJECTING    A    GANTRY 

salient  angle  of  a  wall,  also  any  particular  stone  or  brick 
composing  it. 

The  Builder's  Gantry,  page  93,  is  a  structure  used 
in  large  towns,  where  there  is  much  traffic,  for  the  purpose 
of  carrying  the  scaffolding,  used  in  erecting  the  walls  of 
buildings,  well  above  the  heads  of  pedestrians,  the  scaffold 
proper  starting  from  the  platform  shown  in  the  drawing, 
which  is  raised  some  10  or  12  ft.  above  the  pavement. 
It  is  composed  of  stout  timbers  from  7  in.  square  to  n  in. 
square,  according  to  the  spacing  and  load  to  be  carried, 
secured  together  with  timber  dogs.  In  some  few  instances 
where  the  job  is  expected  to  last  some  years,  the  standards 
or  uprights  are  framed  and  tenoned  into  the  heads  and  sills. 
The  platform  is  composed  of  deals  such  as  are  used  for  floor 
joists,  and  they  are  lightly  spiked  to  the  heads.  A  light 
sloping  guard  or  "  fan  "  is  run  around  the  front  and  ends  to 
prevent  material  falling  into  the  street. 

To  draw  the  gantry,  commence  by  projecting  the  rect- 
angle, a-b-c-d,  shown  in  dotted  lines,  at  an  angle  of  30°,  with 
the  horizontal  to  the  left,  and  another  rectangle  level  with 
the  floor,  towards  the  right ;  these  two  rectangles,  placed 
isometrically,  will  contain  the  main  structure,  and  the  various 
dimensions  can  be  scaled  off  upon  the  root  lines.  The  chief 
dimensions  are  :  height,  pavement  to  floor,  u  ft. ;  width  out 
to  out  of  standards,  9  ft. ;  distance  between  standards  in 
front,  9  ft.  ;  space  between  joists,  i  ft.  3  in.  ;  height  of 
handrail,  3  ft.  ;  height  of  braces,  6  ft.  6  in. 

The  Draper's  Counter  shown  on  page  95,  also  ortho- 
graphically  on  page  70,  will  test  the  student's  carefulness, 
and  if  he  does  not  work  accurately  to  previous  instruc- 
tions as  to  measuring  off  the  details  upon  the  root  lines  and 
projecting  them  into  the  picture  where  required,  he  need  not 
hope  to  succeed  in  producing  a  correct  isometric  projection. 
Portions  of  the  top  and  the  front  framing  are  supposed  to  be 
cut  away  so  that  the  interior  construction  can  be  seen.  It 
is  perhaps  scarcely  necessary  to  say  that  the  counter  will  not 
be  so  made,  and  the  parts  shown  removed  will  be  continued, 


96  A    DRAPER'S    COUNTER 

as  indicated  by  the  dotted  lines.  The  front  of  this  counter 
is  made  of  ij  yellow  deal ;  each  section  is  framed  in  one  piece 
with  stiles  at  the  ends  running  to  the  floor,  the  intermediate 
mountings  stub  tenoning  into  the  rails.  The  bottom  rail 
finishes  about  3  in.  below  the  plinth,  which  is  fixed  to  blocks 
or  "  backings  "  nailed  upon  the  divisions.  The  plinth  or 
skirting  runs  across  the  door  in  the  return  end,  and  is  cut  at 
a  bevel  in  the  joints,  as  shown  in  Fig.  7,  page  70,  to  pass 
clear.  The  top  has  a  considerable  overhang  in  front  and 
is  thickened  outside  with  a  moulded  lining  screwed  on  ;  it 
is  secured  by  slipping-buttons  fitting  into  grooves  in  the 
tilting  pieces  and  screwed  underneath  ;  this  is  to  prevent 
splitting,  which  such  a  wide  board  would  be  liable  to  do  if 
fixed  immovably. 

The  carcase  is  constructed  by  forming  tenons  upon  the 
top  ends  of  the  divisions  in  a  notch  cut  to  receive  the  back 
rail,  and  at  the  lower  end  they  are  housed  or  grooved  to 
receive  the  f  in.  bottom,  which  is  secured  by  gluing  angle 
blocks  beneath,  the  intermediate  rails  forming  divisions  for 
the  drawers,  double  tenoned  into  the  divisions  at  each  end, 
and  the  runners  are  single  tenoned  into  them  for  J  in.,  also 
housed  f\  in.  into  the  uprights.  As  a  rule,  dust  boards  are 
not  provided  in  these  counters  ;  if  they  were  required  they 
would  be  inserted  in  grooves  similar  to  those  in  the  tilting 
pieces. 

To  draw  this  example  start  at  A— A,  which  represents  the 
salient  angle  of  the  front  framing  or  mitre  marked  M  in 
Fig.  i,  page  70.  Set  off  on  this  .the  height  to  the  under  side 
of  the  top,  and  project  the  dotted  lines  to  left  and  right, 
forming  the  root  lines,  and,  working  from  the  plan  on  page 
70,  space  out  the  dimensions  of  the  divisions,  thickness 
of  the  front,  etc.  It  would  be  both  wearisome  to  read  and 
probably  useless  to  give  instructions  for  placing  every  detail 
in  the  picture,  as  words  would  give  no  clearer  description 
than  the  drawing  itself. 

Circles  and  Curves. — When  a  circle  is  projected 
isometrically  it  becomes  an  ellipse,  or,  to  state  the  facts  with 


98  CIRCLES    IN    ISOMETRIC 

more  exactness  of  expression,  an  ellipse  in  an  isometric 
projection  represents  a  circle  in  either  plan  or  elevation, 
and,  from  the  association  of  ideas  consequent  upon  the 
observation  of  natural  phenomena,  the  mind  invariably 
assumes  that  a  circle  is  represented  when  the  ellipse  is 
rendered  isometrically.  Therefore  it  follows  that  if  we  desire 
to  suggest  an  elliptic  solid  isometrically  the  only  way  in 
which  we  can  differentiate  it  from  a  cylinder  is  to  label  it. 
The  readiest  method  of  rendering  the  circle  isometrically 
is,  as  advised  for  projecting  polygons,  to  enclose  it  within  a 
square,  and  to  draw  projectors  from  various  points  in  the 
curve  to  the  sides  of  the  square,  then  to  redraw  the  square 
in  the  form  of  a  rhombus,  by  projecting  its  sides  at  an  angle 
of  30°  with  the  horizontal,  thereafter  transferring  the  pro- 
jected points  from  the  sides  of  the  square  to  the  correspond- 
ing sides  of  the  rhombus,  and  then  drawing  from  these  points 
lines  parallel  with  the  root  lines,  locating  the  points  in  the 
curve  upon  them  from  the  original  drawing  and  tracing  the 
elliptic  curve  through  these.  The  method  is  shown  on 
page  97.  Fig.  I  is  the  circle  to  be  shown  isometrically. 
Proceed  to  enclose  it  within  the  square  a-b-c-d,  whose  sides 
are  made  to  touch  the  circle.  Draw  the  diagonals  a-c  and 
b-d,  also  the  transverse  diameters  1-3  and  2-4.  These  lines 
will  locate  eight  points  in  the  curve ;  if  more  are  required,  any 
number  of  intermediate  points  may  be  plotted  by  projectors 
perpendicular  to  the  sides  as  shown  at  o,  x,  y.  Fig.  2 
shows  the  square  in  isometric  projection  when  it  becomes  a 
rhombus.  The  various  perpendiculars  are  transferred  from 
Fig.  i  to  Fig.  2,  where  they  are  similarly  numbered  and  their 
lengths  marked — i.e.  the  distance  from  the  adjacent  side  of 
the  square  that  the  original  curve  passes  through  them — 
and  the  curve  can  then  be  drawn  through  these  points. 
Fig.  3  shows  the  method  of  placing  the  circle  in  the  vertical 
plane.  If  this  is  projected  in  the  usual  manner  from  the  T-- 
square held  horizontal,  the  set  square  of  60°  should  be  used 
to  project  the  sides  of  the  containing  square  a-b-c-d,  and 
the  diagonal  b-d  becomes  the  major  axis  of  the  ellipse.  If 


COMPLEX    CURVES  99 

preferred,  the  paper  may  be  turned  around  until  b-d  lies 
horizontal,  when  the  usual  projectors  at  30°,  as  shown  at  a, 
may  be  used.  As  the  completion  of  this  end  is  merely  a 
repeat  of  Fig.  2  no  further  instructions  should  be  necessary. 

We  may  convert  the  plane  figure  into  a  solid  by  producing 
the  angles  of  the  square  to  the  required  distance  in  a 
horizontal  direction,  and  drawing  its  repeat  to  form  the 
distant  end.  For  the  purpose  of  projecting  the  cylinder, 
only  one  half  of  the  square  need  be  drawn,  as  the  view  of  the 
distant  side  will  be  intercepted  by  the  cylinder. 

Having  drawn  the  half -square  as  shown,  carry  the  various 
measuring  points  across  the  sides  of  the  prism  as  indicated 
by  the  dotted  lines,  and  project  them  across  the  end  to 
discover  similar  points  in  the  curve  to  those  at  the  front  end. 
The  completion  of  the  figure  will  then  be  easy.  Of  course, 
when  the  desired  cylinder  is  obtained  the  various  construc- 
tion lines  are  removed. 

More  Complex  Curves  (as  Fig.  5,  a  short  length  of 
architrave  moulding)  can  be  easily  projected  by  a  similar 
procedure.  Enclose  the  orthographic  section,  Fig.  4,  within 
a  rectangle  touching  its  boundaries,  and  draw  perpendiculars 
to  the  sides  from  the  various  angles  and  points  in  the  curves  ; 
number  these  for  ready  reference  and  proceed  to  place  the 
rectangle  into  isometric  projection,  its  base  and  edges  form- 
ing the  root  lines  as  shown  in  Fig.  5.  Then  transfer  the 
various  points,  and  number  to  correspond  with  the  original. 
Project  these  across  each  face  with  the  set  square  of  30°, 
and  mark  off  their  various  lengths,  which  give  all  the  neces- 
sary points  for  completing  the  view,  that  should  be  clear 
by  an  inspection  of  the  figures. 


CHAPTER  VII 
OBLIQUE    PROJECTION 

Limitations,  Types,  Description  of  the  "  Single  Scale  "  Method 
— its  essential  defect.  "Half  Scale"  Projection — its  dangers, 
suitability  for  school  demonstrations.  The  "  Official  "  Method. 
Theory  of  Oblique  Projection  illustrated.  Examples — cubes 
and  prisms.  A  Trussed  Partition — details  of  construction. 
A  New  Method — Diminished  oblique  projection,  its  advantages. 
An  Oblique  Scale — how  to  construct  it.  A  Ventilating  Grating 
— details  of  joints.  Method  of  constructing  Pentagons. 
Projection  of  a  pentagonal  Prism.  Shuttering  and  Forms 
in  Reinforced  Concrete  Work.  The  Carpenter's  last  resource. 
Material  to  use.  Size  of  Forms.  How  to  construct  them. 
Cleats  and  Props.  Method  of  Drawing 

THIS  method  of  drawing  is  probably  the  easiest  to  learn 
and  the  simplest  to  use,  for  illustrative  purposes,  of  any, 
and  it  is  to  be  regretted  that,  except  in  the  case  of  objects 
with  a  fairly  simple  outline,  it  cannot  be  used  for  "  work- 
shop drawings" — i.e.  drawings  from  which  the  sizes  can 
be  transferred  directly  to  the  material.  The  reason  of  this 
will  presently  be  obvious.  It  has  already  been  stated  in 
Chapter  I.  that  there  are  three  varieties  of  this  description 
of  projection  in  general  use,  and  the  author  ventures  to 
offer  a  fourth  in  the  examples  on  page  107,  which,  though 
limited  in  its  scope,  gives,  he  thinks,  a  somewhat  improved 
effect  to  the  drawings  for  which  it  is  suitable. 

In  the  first  method  of  oblique  projection,  the  chief  face 
or  elevation  of  the  object  is  drawn,  as  in  orthographic 
projection,  upon  a  plane  parallel  to  the  observer,  and  the 
receding  surfaces  are  drawn  at  any  convenient  angle,  but 
always  in  parallel  pairs  ;  for  this  reason  the  method  has 
been  somewhat  loosely  described  as  "  parallel  perspective." 

100 


102  HALF    SCALE    OBLIQUE 

The  rear  face  is  made  parallel  to  the  front  one.  Figs,  i  and 
2,  page  101,  are  the  orthographic  projections  of  a  cube 
introduced  for  the  sake  of  comparison,  and  Figs.  3,  4  and 
5  are  oblique  projections  of  the  solid  at  different  angles, 
and  the  methods  of  producing  them  will  be  so  obvious  as  to 
need  no  description.  It  will  be  noted  that  all  of  the  retiring 
projectors  are  at  angles  other  than  right  angles,  hence  the 
term  "  oblique." 

A  person  to  whom  this  method  of  projection  is  unfamiliar 
will  doubtless  conclude  from  the  appearance  of  Figs.  3,  4 
and  5  that  the  oblique  side  is  shown  much  longer  than  the 
front.  Of  course  in  a  "  cube  "  all  the  sides  are  alike,  as 
shown  in  Figs.  I  and  2,  and  if  these  drawings  are  tested 
with  compasses  they  will  be  found  so.  This  false  appear- 
ance is  the  essential  defect  of  the  method  ;  and  that  next 
to  be  described  is  devised  to  counteract  it. 

Half-Scale  Oblique  Projection. — In  this  method,  which 
is  shown  in  Figs.  6  and  8,  the  front  elevation  is  drawn  as 
before,  either  full  size  or  to  some  definite  scale,  but  the 
measurements  made  upon  the  oblique  projectors  are  to  half 
full  size  or  half  scale,  as  the  case  may  be.  All  lines  which 
are  parallel  to  the  front,  however,  are  kept  to  the  same 
scale  throughout.  This  method  undoubtedly  gives  a  more 
correct  impression  of  the  solid  than  the  first  method,  but 
the  introduction  of  the  second  scale  renders  extreme  care 
on  the  part  of  the  user  necessary,  to  avoid  errors  in  working 
to  the  measurements. 

Oblique  projection  drawing  is  much  used  in  schools  and 
at  classes  for  manual  training,  as  it  lends  itself  readily  to 
blackboard  demonstration  purposes,  and,  in  or  about  1896, 
the  chief  authority  on  the  latter  subject,  the  City  and 
Guilds  of  London  Institute,  attempted  to  place  the  method 
upon  a  scientific  basis.  They  published,  in  their  "  pro- 
gramme "  of  that  date,  a  method  and  theory  that  would  be 
accepted  at  their  examinations  for  manual  training  teachers' 
certificates  ;  the  method  is  shown  in  Fig.  7,  illustrating 
the  theory  of  oblique  projection.  The  object  to  be 


THEORY    OF    OBLIQUE    PROJECTION  103 

drawn  (in  the  example,  a  small  clip  or  button)  is  shown 
pictorially  in  space.  The  plane  upon  which  it  is  to  be 
projected,  represented  by  the  rectangle  1-2-3-4,  stands 
vertically  behind,  and  parallel  with,  the  object ;  projectors 
are  taken  from  each  corner  of  the  face  of  the  object,  at  an 
angle  of  45°  with  the  horizontal  line  1-4,  until  they  meet 
the  plane  of  projection.  These  points  of  impingement  are 
joined  by  straight  lines  which  are  parallel  with  the  edges 
they  represent  on  the  object,  thus  an  exact  replica  of  the 
face  of  the  object  is  obtained.  Next,  at  one  of  the  salient 
angles  in  the  picture,  an  arbitrary  projector  is  drawn,  such 
as  a-a"  or  b-b."  This  projector  determines  the  angle  of 
the  visible  sides,  therefore  all  parallel  edges  are  projected 
parallel  with  it,  and  the  depth  or  thickness  of  the  projection 
is  determined  by  drawing  projectors  to  intersect  these,  at 
an  angle  of  45°  from  the  points  on  the  rear  face  of  the  object, 
as  a'-b',  etc. 

This  method  could  be  adapted  to  give  a  projection  with 
the  object  lying  at  any  angle  to  the  plane  of  projection, 
but  no  good  purpose  would  seem  to  be  served  by  it  except 
as  a  mental  exercise,  because  the  object  must  first  be  drawn 
pictorially,  when  the  projection  seems  superfluous.  Fig.  8 
on  this  plate  is  an  example  drawn  in  the  half-scale  method 
of  a  cube  placed  in  the  middle  of  a  slab,  and  resting  upon 
one  edge,  with  its  adjacent  sides  at  an  angle  of  45°  with  the 
surface  rested  upon.  The  slab  is  first  drawn,  also  a  pro- 
jector from  the  middle  of  the  edge  a  ;  upon  this  is  located 
the  position  of  the  face  of  the  cube  which  is  drawn  by  aid 
of  the  set  square  of  45°,  the  oblique  sides  being  projected 
at  30°  and  made  half  the  depth  of  the  front  sides.  Fig.  9 
is  the  projection  of  a  box  by  the  first  method,  to  a  scale 
of  J  in.  to  i  ft. ;  it  should  offer  no  difficulty  as  it  is  merely 
an  elaboration  of  the  cube. 

Fig.  10  is  a  projection  of  a  hexagonal  prism.  The  near 
surface  or  end  is  produced  by  using  the  set  square  of  30° 
to  draw  the  two  lower  surfaces,  marking  upon  them  the 
required  width,  raising  vertical  sides  at  these  points,  making 


DIMINISHED    OBLIQUE    PROJECTION  105 

these  the  same  length  as  the  first ;  then  slide  the  set  square 
forward  until  it  reaches  the  ends  of  the  vertical  sides,  and 
lines  drawn  therefrom  will  complete  the  hexagon.  The 
oblique  projectors  are  at  an  angle  of  45°. 

A  Trussed  Partition,  such  as  is  used  to  divide  large  and 
lofty  buildings  into  apartments,  is  shown  in  oblique  pro- 
jection on  page  104,  and  a  portion  of  the  head  of  an  open- 
ing in  a  similar  partition  is  shown  below.  The  former  is 
projected  from  the  elevation  at  an  angle  of  30°,  the  latter 


Oblique  Projection— a  Doorway  in  a  Framed  Partition 

at  45°.  The  opening  shows  linings  to  receive  a  door  with 
portion  of  the  architrave  grounds  attached  to  indicate 
method  of  fixing  them.  The  cross  or  counterlaths  C.C.C. 
are  fixed  to  the  face  of  the  framing,  to  provide  a  space 
behind  the  ordinary  laths  to  receive  the  key  of  the  plaster. 

The  elevation  in  both  cases  should  be  completed  in  the 
usual  manner  before  setting  them  into  oblique. 

Diminished  Oblique  Projection. — The  author  would 
distinguish  by  the  above  term  a  method  of  placing  objects 
in  oblique  projection  that  he  has  used  in  his  classes  for 
some  years  with  success.  The  view  obtained  is  clear  and 


106  AN    OBLIQUE    SCALE 

convincing,  and  does  not  offend  one's  sense  of  proportion,  as 
do  drawings  by  the  common  method.  Within  well-defined 
limits  it  gives  very  rational  graphs  of  polygonal  and  other 
than  rectangular  figures,  which  are  difficult  of  representa- 
tion by  other  methods,  and  it  has  the  advantage  that  the 
oblique  sides  are  diminished  in  a  definite  and  constant 
ratio  to  the  parallel  sides.  Moreover,  no  scale  need  be  used 
to  read  the  dimensions  ;  all  that  is  necessary  to  discover  the 
dimensions  of  any  part  is  to  project  a  parallel  from  it  to 


Peal 
Method  of  constructing  an  Oblique  Scale 

the  ground  or  picture  line,  when  it  is  at  once  seen  in  its 
true  size,  or  to  the  same  scale  that  the  parallel  portion  is 
drawn.  The  method  will  be  made  clear  in  the  description 
of  the  examples.  If,  however,  it  is  preferred  to  use  a  scale 
for  taking  the  dimensions,  one  can  easily  be  constructed  as 
shown  above.  Thus,  lay  down  the  real  scale,  or  a  full-size 
measure,  horizontally,  and  from  its  left  extremity  draw  a 
line  at  an  angle  of  45°  (or  whatever  angle  it  is  intended  to 
use),  and  upon  this  line  draw  projectors  at  reverse  angle, 
from  each  division  upon  the  real  scale,  and  a  scale  con- 
tracted as  shown  will  indicate  the  real  dimensions  when  it 
is  applied  to  the  oblique  drawing. 


108  A    SHIP'S    GRATING 

Fig.  I,  page  107,  is  the  plan  in  orthographic  projection 
of  a  wood  grating  or  ventilator  used  for  covering  openings 
in  floors,  decks,  etc.  Fig.  2  is  a  view  of  the  same  object 
placed  in  oblique  projection  by  the  diminishing  method. 

The  front  edge  of  the  frame  is  drawn  resting  on  the  ground, 
and  the  ground  line  is  produced  to  the  left  indefinitely. 
Project  the  two  ends  of  the  frame  at  angles  of  45°  with  the 
ground  line,  then  set  off  on  the  ground  line  to  the  left  of 
angle  a',  the  point  b',  equal  to  the  width  of  the  frame  a-b, 
Fig.  i.  It  is  perhaps  unnecessary  to  say  that  this  plan  is 
only  drawn  for  the  purpose  of  explaining  the  method  clearly, 
and  that  the  view  could  be  made  equally  well  from  written 
data.  Having  obtained  point  b',  project  a  line  from  it  at  an 
angle  of  45°,  intersecting  the  first  drawn  projector  at  point 
b" ;  this  locates  the  back  edge  of  the  frame,  and  defines  its 
width.  Complete  the  outline  of  frame.  Next  set  off  the 
widths  of  the  bars  and  spaces  along  the  top  edge  as  shown, 
also  along  the  ground  line  for  the  end,  as  indicated  by  the 
figures  i  to  8 ;  project  these  respectively  parallel  with  the 
ends  and  the  line  b'-b",  by  aid  of  the  set  square  of  45°,  and 
carry  the  latter  vertically  to  the  upper  surface,  when  the 
completion  of  the  grid  will  be  a  simple  matter.  The  inter- 
secting angles  are  to  be  shown  as  in  the  drawing,  and  a  little 
shading  introduced  to  give  the  effect  of  solidity  ;  the  light 
is  supposed  to  come  from  the  right  hand. 

Details  of  the  Joints  are  shown  in  Fig.  3  by  the  same 
method,  but  the  construction  lines  are  removed.  The 
piece  A  is  shown  beneath  B,  instead  of  above  it,  for  want 
of  space ;  otherwise  it  is  relatively  in  the  correct  position. 
An  angle  of  45°  is  generally  the  best  for  this  method  of 
projection,  but  any  other  convenient  angle  may  be  used, 
if  it  is  remembered  that  the  diminishing  projectors  must 
always  be  at  a  similar  angle  reversed. 

Pentagons.— The  application  of  the  method  for  pro- 
jecting polygonal  figures  is  shown  in  Fig.  5.  It  may  be 
useful  first  to  give  a  method  of  constructing  a  pentagon 
geometrically.  Let  A-B,  Fig.  4,  be  the  given  side  of  the 


no  CONSTRUCTING    PENTAGONS 

pentagon.  At  B,  erect  a  perpendicular,  and  make  it  equal 
to  the  given  side;  bisect  A-B,  and  from  its  centre  c,  with 
radius  c-d,  describe  the  arc  d-e.  Then  from  A  and  B  as 
centres,  and  A-e  as  radius,  describe  arcs  intersecting  in  E. 
From  points  A-B-E,  with  radius  A-B,  draw  intersecting 
arcs.  Join  up  the  points  of  intersection  and  the  pentagon 
will  be  constructed. 

To  construct  an  Oblique  Projection  of  a  Pentagonal 
Prism,  Fig.  5. — Draw  the  ground  line,  and  upon  it  construct 
one  face  of  the  prism,  as  A'-a-b-B'-A' '.  Draw  the  projector 
c'-E  at  angle  of  45°.  We  have  next  to  find  its  length.  Set 
the  height  of  the  pentagon  C-E  (Fig.  4)  off  on  the  ground 
line  from  C'  to  E' ',  and  draw  a  projector  from  this  point, 
intersecting  the  first  at  E.  We  have  now  the  diminished 
height  of  the  pentagon,  and  as  all  the  points  will  be  similar 
at  the  other  end  of  the  prism,  erect  a  perpendicular  (dotted) 
at  E,  and  make  it  equal  in  length  to  A  '-a.  We  have  next 
to  place  the  inclined  sides  in  their  relative  position.  We 
might  do  this  by  finding  a  proportional  at  right  angles  to 
the  line  c'-E  as  shown  at  the  top  end,  and  so  locating  the 
two  side  angles,  but  it  is  easier  to  deal  with  the  side  in  re- 
lation to  a  right  angle.  Draw  a  dotted  projector  from  B'. 
Next  draw  a  perpendicular  to  B-d,  Fig.  4,  from  the  angle 
F,  intersecting  B-d  in  i.  Set  off  B-i  along  the  ground  line 
from  B'  and  draw  a  projector  from  i.  This  gives  the 
diminished  length  of  B-i,  and  on  a  parallel  to  the  ground 
line  through  the  intersection  we  can  locate  point  /,  which 
represents  F  in  Fig.  4.  Points  B'-f  and  E  can  now  be 
joined  up  and  the  two  sides  drawn.  To  obtain  the  opposite 
angle,  draw  a  horizontal  line  from  /,  and  intersect  it  by  a 
projector  from  h",  which  is  made  the  same  distance  from 
A'  that  h  is  from  A  in  Fig.  4. 

Shuttering  and  Forms  for  Reinforced  Concrete 
Work,  page  109.— These  are  the  terms  applied  to  the 
wood  moulds  or  casings,  erected  to  contain  and  support  the 
concrete  which  is  poured  around  the  iron  bars  and  straps 
composing  the  reinforcement,  until  the  concrete  has 


FORMS  AND  SHUTTERS  FOR  CONCRETE  in 

"set."  The  term  "  shuttering  "  is  applied  to  boards  which 
are  secured  together  with  ledges,  having  merely  to  support 
the  concrete,  such  as  against  the  face  of  walls  or  under  sides 
of  ceilings,  fronts  of  galleries,  etc.  When  the  duty  of  the 
casing  is  to  mould  or  shape  the  concrete  poured  into  it,  as 
in  the  case  of  girders  and  columns,  it  is  termed  "  forms/' 
Both  kinds  are  shown  in  the  illustration,  which  is  given  as 
an  advanced  example  of  diminished  oblique  projection. 

The  objects  of  these  constructions  are  that  they  shall  be 
economical  in  cost  of  construction,  shall  be  readily  removable 
without  damage  to  the  green  work,  and  shall  be  strong 
enough  to  support  the  loads  without  deflection,  and  shall 
not  cast  or  warp  on  the  introduction  of  the  wet  concrete. 
Various  methods  and  devices  are  used  to  meet  these  ends,  and 
the  best  must  be  determined  by  individual  circumstances. 

As  at  the  present  time  almost  all  that  is  left  for  the  car- 
penter to  do  on  modern  buildings  is  the  formation  of  these 
casings,  it  may  not  be  out  of  place  to  offer  a  few  remarks  upon 
their  construction.  The  wood  selected  should  not  be  the 
roughest  and  commonest  that  can  be  obtained.  Whilst  it 
is  not  suggested  that  first-class  joiner's  wood  should  be 
used,  the  cost  for  labour  in  conversion  and  subsequent 
making  good  of  defects  on  the  face  of  the  work  will,  if  any 
rubbish  is  used  for  the  forms,  soon  outweigh  the  first  saving 
in  cost  of  material.  Dry  stuff  should  not  be  used,  as  it  will 
swell  abnormally  on  the  introduction  of  the  wet  concrete ; 
shaky  stuff  should  be  avoided,  but  sound  knots  may  be  dis- 
regarded; loose  ones  will  supply  undesirable  "  keys  "  that 
will  prevent  removal.  The  fewer  nails  used  the  better. 
These  will  rust  in  and  be  unremovable,  and  as  a  conse- 
quence much  of  the  stuff  would  be  useless  for  conversion. 
The  shuttering  should  not  be  in  too  large  pieces  for  con- 
venient handling ;  joints  in  the  stuff  do  not  matter,  as  the 
surfaces  of  the  concrete,  if  not  rendered,  are  usually  rubbed, 
unless  they  are  out  of  sight. 

Forms  for  beams  should  be  made  so  that  the  sides  can  be 
removed  without  interference  with  the  bottom ;  it  is  often 


H2  FIXING    SHUTTERING 

necessary  to  accelerate  the  drying  by  removing  the  side 
shuttering  as  soon  as  the  concrete  is  sufficiently  set,  yet 
not  strong  enough  to  support  itsc  If,  hence  the  soffit  board 
and  centering  must  be  left  up.  For  this  reason  the 
"  troughs  "  are  not  nailed  together,  but,  as  shown  in  the 
foreground  of  the  drawing,  are  either  wedged  up  tightly 
against  the  bottom  board  or  where  the  "  panel  "  is  not  to  be 
filled  in,  until  the  girders  are  set,  a  method  often  used  in 
heavy  floors,  "  Box  cleats  "  are  formed  around  the  trough, 
letting  the  ends  of  the  ledges  project  slightly  and  notching 
them  into  cross  pieces.  If  a  nail  is  driven  into  the  loose 
.  piece  to  prevent  its  falling  off,  the  head  should  stick  out  for 
the  pincers  to  grip. 

Mouldings  or  chamfers  are  generally  made  on  the  lower 
edges  of  girders  ;  the  shapes  for  these  should  be  nailed 
to  the  bottom,  not  to  the  sides  of  the  forms.  Let  the  ends 
of  the  beam  troughs  rest  upon  notches  cut  in  the  column 
forms  as  shown,  because  the  column  casing  should  always 
be  the  last  removed.  A  good  foreman  will  keep  these  up  as 
long  as  he  can,  to  protect  the  concrete.  The  fixed  ledges 
on  the  "  sides  "  of  the  column  casing  should  run  over  the 
edges  of  the  "  faces."  This  will  keep  them  in  right  position 
when  setting  up  whilst  the  box  cleats  are  being  fixed. 
These  cleats  are  turned  out  in  numbers  from  the  mill,  and 
holes  bored  in  the  tenons  for  the  oak  pins  to  secure  them. 
The  latter  are  kept  in  a  box  handy  to  the  workman,  and  can 
be  used  many  times  over.  Another  form  of  clamp  is  shown 
in  Fig.  2.  These  are  nailed  together  at  the  angles  as  they  are 
placed  around  the  forms,  but  are  only  suitable  for  columns 
of  small  size  or  height.  Near  the  bottom  of  high  columns, 
the  clamps  should  be  made  of  3  in.  x  3  in.  stuff  bolted  at  the 
angles,  as  the  pressure  is  great  at  the  bottom  of  a  column, 
especially  if  it  is  filled  in  quickly. 

Most  of  this  casing  is  shown  as  inch  stuff,  but  the  thick- 
ness will  depend  upon  the  nature  and  size  of  the  beams, 
etc.  The  props  must  be  placed  pretty  closely  together,  so 
that  no  sagging  takes  place.  The  bearers  carrying  the  panels 


FIXING    SHUTTERING  113 

are  shown  as  2  in.  x  6  in.  floor  joisting,  and  the  props 
should  be  notched  over  them  to  prevent  being  knocked 
aside.  This  is  better  than  nailing,  for  the  subsequent  re- 
moval. The  panel  shuttering  should  not  be  fitted  tightly ; 
allowance  should  be  made  for  swelling. 

In  drawing  the  example,  get  in  the  main  features  or  out- 
lines first,  leaving  details  until  later. 

The  column,  being  the  principal  object  in  the  drawing, 
ma}'  well  form  the  starting-point,  then  the  four  troughs. 

Portions  have  been  purposely  omitted  from  the  example 
to  show  the  construction  clearly,  and,  apart  from  the  numer- 
ous details  which  simply  require  carefulness  on  the  part 
of  the  draughtsman  to  place  correctly,  anyone  who  has 
worked  through  the  previous  examples  should  be  able  to 
reproduce  this. 


CHAPTER  VIII 
PERSPECTIVE    OR    RADIAL    PROJECTION 

Definitions  and  Principles.  The  Limiting  Cone  of  Visual  Rays. 
A  Simple  Method  of  producing  a  Perspective  from  the 
Plan — its  limitations.  Examples — with  instructions  for  draw- 
ing. A  Rectangular  Frame.  A  Stone  Pedestal.  A  Large 
Chest.  A  Pedestal  or  Office  Table.  Method  of  determining  the 
Vanishing  Planes — when  a  vanishing  point  is  not  available. 
Obtaining  the  Perspective  Reduction  when  Vanishing  Points 
are  out  of  limit 

THE  method  of  perspective  projection  here  described  is  a 
variation  of  the  more  elaborate  process  used  by  artists  in 
preparing  pictures.  The  principles  involved  are  the  same, 
but  the  method  of  application  is  simplified.  Of  course  the 
method  has  its  limitations,  but  it  has  sufficient  scope  to 
embrace  all  the  requirements  of  the  student  of  technical 
drawing.  The  limits  of  this  book  compel  restriction  to  a 
few  elementary  examples.  The  purpose  of  perspective 
drawing  is  to  represent  objects  as  they  appear  to  the  eye 
when  viewed  in  certain  defined  positions  and  distances  from 
the  observer,  which  is  the  essential  difference  between  this 
class  of  drawing  and  the  others  dealt  with  in  this  book, 
wherein  no  consideration  is  given  to  the  position  or  distance 
of  the  object  represented. 

Definition  of  Terms  and  Symbols  used  in  Perspec- 
tive.—  It  is  assumed  as  a  principle  in  this  form  of  perspective 
drawing  that  rays  of  light  pass  in  straight  lines  from  every 
portion  of  the  object  to  the  eye  of  the  observer,  forming,  as 

114 


THE    PICTURE    PLANE  115 

it  were,  a  cone  of  rays,  the  base  of  which  contains  the  object, 
the  apex  of  the  cone  being  in  the  eye  of  the  observer  ;  if, 
then,  it  is  conceived  that  a  transparent  plane  is  interposed 
between  the  object  and  the  person  viewing  it,  and  that  the 
rays  of  light  passing  through  the  plane  are  connected  by  a 
series  of  lines  on  the  plane,  it  will  be  obvious  that  we  should 
thus  get  a  representation  of  the  object  upon  the  plane,  differ- 
ing in  size  only,  according  to  the  distance  the  plane  is  placed 
from  the  eye. 

This  imaginary  plane  is  the  one  dealt  with  in  making  a 
perspective  drawing,  and  it  is  termed  the  picture  plane, 
usually  denoted  by  the  symbol,  P.P.  Obviously,  the  nearer 
the  picture  plane  is  placed  to  the  object  the  larger  will  be 
the  view  obtained  upon  it ;  also  the  farther  the  observer 
stands  from  the  object  the  smaller  will  it  appear  to  him. 
We  know  by  experience  that  when  a  flag  is  placed  at  the  top 
of  a  tall  mast  it  looks  very  much  smaller  than  when  at  our 
feet  on  the  ground. 

Also  we  know  by  experience  that  if  we  observe  an  object 
obliquely  we  get  a  different  view  or  impression  upon  the 
retina  of  the  eye  than  we  do  when  it  is  seen  from  directly  in 
front.  Now  as  the  purpose  of  a  perspective  drawing  is  to 
represent  the  object  as  it  appears  to  a  person  in  a  certain 
position  and  at  a  specified  distance,  it  will  be  understood 
that  the  first  thing  to  be  done  is  to  map  out  these  various 
data  upon  the  drawing,  which  we  can  then  proceed  to  make 
in  conformity  with  them. 

The  necessary  data  for  commencing  the  drawing  are 
indicated  by  the  diagram  on  page  116,  which  is  a  section,  or 
end  view,  at  right  angles  to  the  P.P.  of  the  drawing  shown 
on  page  117.  As  the  object  of  this  method  is  to  simplify 
procedure,  we  make  two  arbitrary  assumptions  at  the  start : 
first,  that  the  ground  plane  (G.P.)  is  5  feet  below  the  hori- 
zontal plane  (H.P.),  the  reason  being  simply  that  5  feet  is 
the  height  of  the  average  person's  eye  above  the  ground. 
The  second  assumption  is  that  the  nearest  angle  of  the  object 


THEORY    OF  PERSPECTIVE 


touches  the  picture  plane  (P.P. ) .  These  assumptions  enable 
us  to  set  down  at  once  on  the  paper  the  horizontal  line 
(H.L.),  which  is  an  edge- view  of  the  plane  in  which  lie  the 
station-point  (S.P.,)  and  the  central  visual  ray  (C.V.R.), 
which  is  another  name  for  the  axis  of  the  cone  of  rays  before 
referred  to.  The  elevation  of  the  C.V.R.  in  the  perspective 
view  is  called  the  centre  of  vision,  C.V.,  see  page  117. 
We  can  thon  draw  the  G.L.  5  ft.  below  and  also  lay 
down  a  plan  of  the  object  with  a  plan  of  the  P.P. 
touching  one  angle,  and  we  can  draw  a  plan  of  the  C.V.R. 


cv: 


Tlir  Object 


Plane 


3\l 


C.V.R. 


S.P.  or  eye  of 

r^t  Otverrer 
\  must  coincide 


GroiuuL    PLuJtc 


'GJj.  PLuuv  of  StaJion. 

Section  of  Diagram,   p.    117,   perpendicular  to  Picture  Plane 

which  must  be  at  right  angles  with  the  plan  of  the  P.P. 
Next  we  fix  on  plan  the  position  of  the  S.P.  from  the  P.P. 
at  such  a  distance  from  the  object  that  a  cone  of  visual 
rays,  having  a  vertical  angle  of  about  40°  at  the  S.P.,  will 
entirely  envelop  it  (see  Fig.,  page  116).  The  reason  for 
limiting  this  angle  is  that  if  a  much  wider  angle  be  adopted 
there  will  be  an  appearance  of  distortion  in  the  resulting 
perspective  view.  The  student  should  make  a  few  experi- 
ments upon  this  point.  Finally  the  vanishing  points  (V.P.) 
have  to  be  located. 

These  are  points  to  which  parallel  lines  appear  to  converge. 
If  the  parallel  lines  are  horizontal  they  will  appear  to  con- 


I 

o 

c 

£ 


n8  THEORY    OF    PERSPECTIVE 

verge  to  points  upon  the  horizon — that  is  to  say,  in  the  H.L. 
If  they  are  inclined  to  the  horizontal  they  will  converge  to 
points  above  or  below  the  H.L.,  as  the  case  may  be.  If  they 
are  parallel  to  the  picture  plane  they  are  represented  as 
parallel  in  the  perspective,  though  they  only  remain  sensibly 
parallel  within  the  limits  of  the  cone  of  restricted  angle  above 
referred  to.  In  the  form  of  perspective  here  described,  only 
horizontal  and  vertical  lines  are  dealt  with  ;  the  latter,  being 
of  course  parallel  with  the  P.P.,  remain  parallel  in  the 
perspective  view.  The  V.P.'s  for  horizontal  lines  are  found 
by  means  of  the  plan  as  explained  below. 

With  the  above  outline  of  the  theory  as  explanation,  we 
can  now  proceed  to  describe  in  detail  the  construction  of  the 
several  drawings  (pages  117,  121,  123,  125),  each  involving 
different  requirements.  It  will  be  seen  that  the  examples 
given  combine  in  each  case  a  plan,  which  is  set  out  in  its 
required  relation  to  the  P.P. ;  an  elevation,  where  necessary 
to  give  dimensions  not  shown  by  the  plan,  and  the  perspec- 
tive view  itself,  which  is  partly  projected  directly  from  the 
plan  and  partly  set  up  by  means  of  dimensions  taken  from 
the  elevations.  One  and  the  same  line  does  duty  for  the 
plan  of  the  P.P.  and  for  the  G.P.  in  the  perspective  view — • 
that  is,  we,  in  effect,  when  making  the  perspective  drawing, 
assume  that  the  picture  plane  is  rotated  into  the  horizontal 
plane,  as  indicated  by  the  dotted  arc  in  the  diagram,  page 
116  ;  where  G.L.,  which  is  also  the  plan  of  the  picture  plane, 
reaches  g.l.  in  the  horizontal  plane.  This  is  the  position 
shown  on  the  perspective  part  of  the  drawing  on  page  117. 

The  plan  and  the  lines  radiating  therefrom  to  the  S.P. 
could,  of  course,  be  set  out  on  a  separate  piece  of  paper,  and 
the  horizontal  dimensions  on  the  P.P.  could  be  transferred 
to  the  perspective  view  by  "  ticking-off  "  :  this  is  the  usual 
procedure  in  office  work  with  more  complicated  drawings, 
but  the  beginner  will  find  this  method  of  drawing  the 
plan  adjacent  the  perspective  view  and  the  obtaining 
the  dimensions  by  projection  much  clearer. 


METHOD    OF    PROJECTION  119 

To  draw  in  Perspective  a  Rectangular  Frame  lying 
on  the  ground  12  ft.  distant  from  the  observer,  with  its 
salient  angle  directly  opposite,  and  its  sides  making  angles 
of  30°  and  60°  respectively  with  the  picture  plane  (see 
page  117). 

Commence  by  laying  down  the  plan  to  the  given  dimen- 

(P  P  } 
'    '  \ 
H.Lj 

and  touching  the  latter  in  point  a,  which  becomes  the 

centre  of  vision.     Project  this  point  to  a  line  drawn  parallel 

fp  p  \ 
to  the  \    '    '  \  distant  12  ft.,  to  scale,  locating  the  station- 

\H.L.) 

point  thereon.  From  this  point  draw  lines  parallel  with 
the  sides  of  the  frame  a-d  and  a-b,  intersecting  the  H.L., 
which  locate  thereon  the  left-hand  and  right-hand  vanishing 
points  respectively.  Draw  the  ground  line  G.L.  5  ft.  below 
the  H.L.  and  parallel  therewith ;  this  locates  the  picture 
plane,  upon  which  we  can  now  produce  the  projection. 
From  each  corner  of  the  frame  a—b-c-d  draw  projectors  to 
the  S.P.,  stopping  them  when  they  reach  the  horizontal  line 
upon  the  picture  plane,  as  shown  at  a-b'-c'-d'.  Drop 
perpendiculars  from  these  points  to  the  ground  line.  It  will 
be  remembered  that  the  angle  a  is  to  be  in  the  line  of  sight 
and  upon  the  ground,  therefore,  where  the  line  drawn  from 
S.P.  to  a  intersects  the  ground  will  be  the  position  of  a'. 
Next  draw,  from  point  a',  lines  to  the  two  vanishing  points, 
and  the  intersections  of  the  projectors  with  these  ;  in  points 
b2,  d2  and  c2  locate  the  corners  of  the  frame  upon  the 
ground.  The  respective  heights  or  verticals  at  these  points 
are  obtained  by  setting  up  the  height  or  thickness  at  a' 
and  drawing  lines  to  the  vanishing  points  as  shown.  In  like 
manner  any  other  point  in  the  plan  is  first  brought  to  the 
horizontal  line,  then  projected  to  the  ground  and  its  position 
located  upon  the  vanishing  planes. 

A  Stone  Pedestal  in  three  tiers,  with  its  sides  making 
angles  of  34°  and  56°  respectively,  with  the  picture  plane 


120  PERSPECTIVE 

and  its  nearest  corner  2  ft.  to  the  right  of  the  spectator  and 
13  ft.  away  from  him,  is  represented  in  perspective  pro- 
jection on  page  121.  An  elevation  is  given  in  Fig.  I  to 
indicate  dimensions. 

Commence  by  drawing  the  H.L.  in  a  convenient  position 
near  top  of  sheet  and  the  G.L.  5  ft.  distant  therefrom,  and  a 
parallel  at  13  ft.  distant,  on  which  mark  the  station-point 
5.P.  Draw  a  perpendicular  from  this  to  the  H.L.,  locating 
the  C.V.,  and  mark  off  along  the  H.L.  point  I,  two  feet  to  the 
right.  From  this  point  set  out  the  sides  of  the  lower  block, 
making  an  angle  of  34°  and  56°  with  the  H.L.,  and  complete 
the  plan  as  shown.  Locate  the  vanishing  points  as  before 
by  lines  drawn  from  S.P.  parallel  to  the  sides  of  the  plan. 
Draw  projectors  from  each  angle  of  the  plan  towards  the 
station-point,  but  stop  at  H.L.  Drop  a  projector  from  point 
i  to  the  ground  ;  this  locates  the  salient  angle  of  the  lower 
slab,  and  on  it  measure  up  the  height  of  point  //.  (see  Fig.  i) . 
Draw  lines  towards  the  vanishing  points  and  intercept  them 
by  projectors  from  points  2  ft.  and  4  ft.  upon  the  horizontal 
line,  thus  locating  the  position  of  the  distant  corners  of  the 
block  in  the  picture.  To  obtain  the  heights  of  the  second 
block  we  must  mark  off  the  heights  as  given  in  Fig.  i  upon 
the  perpendicular  i-//.,  which  lies  in  the  picture  plane,  and 
therefore  shows  real  heights  ;  then  draw  lines  to  the  left  and 
right  vanishing  points  which,  intercepted  by  the  vertical 
projectors  from  the  said  points  on  H.L.,  will  show  the  heights 
those  points  reach  in  the  distance.  A  few  of  the  projectors 
from  the  plan  are  taken  across  to  the  S.P.  to  indicate  the 
direction,  but  these,  of  course,  are  not  dealt  with  below  the 
H.L.  It  will  be  noticed  that  the  sides  of  the  second  block 
which  stand  within  the  lower  one  are  produced  by  means  of 
dotted  lines  to  the  face  of  the  lower  block,  and  thence 
projected  to  the  H.L.  ;  this  is  necessary  in  all  cases  where 
parts  of  the  object  stand  back  from  the  main  face.  When 
they  are  located  upon  this  face  in  the  perspective  projec- 
tion they  must  be  projected  back  again  into  their  relative 


122  PERSPECTIVE    PROJECTION 

position  to  the  face  by  means  of  projectors  taken  from  the 
points  to  the  other  vanishing  point,  as  shown  on  the 
drawing. 

The  Perspective  Projection  of  a  large  Chest  (page 
123). — -This  simple  object  has  been  selected  to  illustrate 
a  method  of  dispensing  with  the  use  of  one  or  both  vanishing 
points  when  the  angle  is  so  low  that  it  takes  these  beyond 
the  drawing  sheet.  Fig.  I  is  the  end  elevation  of  the 
chest  from  which  the  necessary  dimensions  are  obtained, 
Fig.  2  is  the  plan  of  the  chest  in  its  relative  position  to 
the  observer,  and  Fig.  3  is  the  perspective  projection.  To 
simplify  the  explanation  one  vanishing  point  is  shown  on 
the  right  hand ;  the  other  is  outside  the  picture. 

We  will  assume  that  the  projection  has  been  made  in 
accordance  with  previous  instructions  up  to  the  point  where 
position  of  the  two  vanishing  points  has  to  be  located. 
The  plan  of  the  right-hand  vanishing  plane  is  drawn  from 
the  station-point  parallel  to  the  right-hand  side  of  the  plan, 
and  its  intersection  with  the  H.L.  gives  the  R.  V.P.  A  line  is 
also  drawn  from  S.P.  parallel  to  the  left-hand  side  of  the  plan, 
so  far  as  the  limits  of  the  paper  allow.  At  any  convenient 
point  in  this  line,  as  A,  erect  a  perpendicular  to  the  H.L., 
and  at  an  equal  distance  from  the  line  of  sight  on  the 
right  vanishing  plane,  erect  a  similar  perpendicular,  as  at 
B.  Now  the  angles  on  either  side  of  the  line  P.V.  or  S.C.  are 
alike,  and  any  divisions  of  the  base  line  P.V.,  drawn  to  the 
apex  of  the  triangle R.V.P., divides  the  parallel  B  in  the  same 
proportion  that  the  whole  length  of  B  is  to  P.V.  It  follows 
that,  as  the  angles  on  the  left  side  of  P.V.  are  similar  and 
equal  to  those  on  the  right,  any  proportions  upon  the  parallel 
A  will  be  similar  and  equal  to  those  upon  B,  if  drawn  from 
the-  same  points  in  the  base  ;  therefore,  all  that  is  necessary 
to  obtain  corresponding  reductions  in  the  left  vanishing 
plane  to  those  in  the  right  is  to  make  the  divisions  on  A 
equal  to  those  upon  B,  and  draw  lines  to  those  points  from 
the  heights  marked  upon  the  vertical  angle  of  the  object 


124  A    PEDESTAL    TABLE 

which  touches  the  picture  plane.  For  example,  take  the 
point  i  in  line  B.  Where  the  projector  from  the  top  edge  of 
the  chest  passes  through  it,  draw  a  horizontal  line  from  this 
point  to  line  A,  intersecting  it  at  point  i',  and  a  line  drawn 
from  the  front  top  angle  of  the  chest  through  this  point  will 
give  the  angle  of  vanishing  projector  as  correctly  as  if  it 
were  drawn  to  a  vanishing  point.  All  the  other  points 
found  on  B  can  be  projected  in  like  manner  to  A . 

The  Pedestal  Table  shown  in  plan  and  elevation  in 
Figs,  i  and  2,  page  125,  and  in  perspective  in  Fig.  3,  is  an 
example  of  the  method  of  making  the  projection  when  the 
vanishing  point  is  too  distant  to  find  and  the  angles  of  the 
plan  are  unequal.  In  this  case  the  plan  makes  angles  of 
30°  and  60°  with  the  horizontal  line,  and  the  object  is  13  ft. 
from  the  observer.  In  the  previous  case,  where  one  V.P. 
was  missing,  the  position  of  the  plan  enabled  us  to  form  two 
proportionate  triangles  alike  on  each  side  of  the  common 
"  base  "  line.  Here  that  method  cannot  be  followed,  but 
we  can  proceed  to  locate  the  left  vanishing  point  which  lies 
within  the  picture,  and  so  obtain  a  triangle  in  which  we  can 
arrange  a  smaller  one,  as  at  A-a,  L.V.P. 

We  can,  with  this  as  a  base,  construct  a  similar  triangle 
on  the  other  side,  which  shall  bear  the  same  relation  to  the 
hypotenuse  of  that  triangle  as  A-a  does  to  the  line  S.P- 
L.V.P.  Then  all  reductions  obtai  led  upon  A—a,  if  trans- 
ferred to  the  proportionate  parallel  B-b,  will  give  proper 
reductions  for  that  side  of  the  picture,  and  we  shall  obtain 
exactly  the  same  lines  as  if  we  had  taken  them  directly  to  a 
vanishing  point  upon  that  side. 

Proceed  to  lay  down  the  plan,  the  H.L  and  G.L.,  and  the 
station-point,  to  given  data  and  draw  the  plans  of  the 
vanishing  planes  as  far  as  possible,  and  parallel  the  re- 
spective sides  of  the  plan.  Anywhere  on  L.V.P.-S.P. 
erect  a  perpendicular  to  the  H.L.,  as  A  -a.  Draw  a  parallel 
to  the  H.L.  from  A,  intersecting  the  right  vanishing  plane  in 
B  ;  erect  a  perpendicular  to  H.L.,  and  transfer  all  reduced 


126  A    PEDESTAL   TABLE 

points  on  A-a  to  B-b,  as  shown,  and  thus  obtain  direction 
of  vanishing  lines  upon  that  side. 

The  completion  of  the  perspective  view  will  now  proceed 
as  described  in  previous  cases,  the  heights  of  the  drawers, 
plinths  and  door  rails  being  obtained  from  the  elevation, 
Fig.  2.  A  scale  of  feet  is  provided  by  aid  of  which  the 
sizes  may  be  read  off. 


CHAPTER  IX 
FREEHAND    DRAWING   OR   SKETCHING 

Definition  of  Freehand — its  uses  to  the  artisan  and  draughts- 
man. How  to  draw  Curves.  Manipulation  of  the  Pencil. 
Plotting  Points.  Examples — copying  a  moulding,  a  cabinet 
screw  driver,  cylinders.  A  Stone  Baluster.  A  Screw  Wrench. 
Use  of  Squared  Paper — enlarging  and  diminishing  drawings. 
Sectional  Tracing  Paper — how  to  use  it.  Stone  Carving 
for  a  Window  Head.  Various  Hinges — description  of  their 
uses  and  sizes  :  butt,  back  flap,  table  and  desk  hinges, 
trestle,  parliament,  pew,  counter  flap,  hook  and  eye,  Collinge, 
cross  garnets,  floor  springs 

THE  term  "  freehand  "  has  been  denned  in  Chapter  I.,  and 
it  is  only  necessary  to  say  here  that  what  is  meant  and 
described  under  that  term  is  the  production  by  pen  or  pencil 
of  those  parts  of  a  technical  drawing  that  cannot  profitably 
be  made  by  means  of  instruments.  There  are  many  small 
and  subtle  curves  met  with  in  technical  drawing  that  can 
be  quickly  and  well  put  in  by  the  unaided  pen  or  pencil  if 
the  draughtsman  educates  his  hand  to  that  end,  and  it  is  to 
assist  him  in  acquiring  this  power  that  these  instructions  are 
given.  Straight  lines  can  be  better  and  more  profitably 
produced  by  mechanical  aids,  and  though  the  power  to  draw 
a  straight  line  a  foot  long  entirely  without  the  help  of  a 
ruler,  etc.,  may  be  of  value  on  rare  occasions,  it  seems  to  the 
author  that  time  can  be  better  spent  than  in  attempting  to 
acquire  such  exceptional  skill,  and  he  prefers  to  use  instru- 
ments for  the  purpose  himself.  The  ability  to  draw  a  firm 
regular  line,  showing  the  profile  of  a  moulding,  or  to  sketch 
some  small  object  we  wish  to  describe  is  of  value  to  every 
artisan,  and  not  the  least  to  those  who  aspire  to  positions 
of  authority  or  supervision. 
127 


128  HOW    TO    STARTj  FREEH  AND 

The  methods  here  described  are  those  used  by  the  author 
for  many  years. 

How  to  draw  a  Curved  Line. — The  beginner  generally 
starts  off  to  draw  a  curved  line  by  gripping  the  pencil  rigidly 
between  thumb  and  fingers  in  a  nearly  upright  position, 
and,  with  stiffly  set  wrist,  proceeds  to  trail  slowly  across  the 
paper,  in  as  near  as  may  be  the  direction  desired.  In- 
variable result :  a  weak,  wobbly  and  irregular  line,  which, 
if  unadvised,  he  disgustedly  rubs  out  and  begins  afresh  in 
the  same  manner  !  Nothing  else  might  be  expected,  the 
tense  muscles  causing  continual  vibration  of  the  hand. 

Quite  the  opposite  of  the  above  method  is  the  correct 
one.  The  pencil  should  be  held  as  lightly  as  possible,  much 
as  one  does  in  writing,  with  the  fingers  and  thumb  working 
in  unison,  not  counteracting  or  checking  each  other.  The 
particular  slope  or  angle  of  the  pencil  is  of  less  moment, 
and  will  vary  with  individual  habits,  also,  to  some  extent, 
with  the  size  of  the  curve  to  be  drawn.  For  large,  bold 
sweeps,  an  angle  as  shown  in  Fig.  4,  page  129,  is  suitable, 
very  similar  to  that  of  a  pen  in  writing.  Smaller  curves 
will  need  the  pencil  held  more  uprightly,  so  that  the  point 
shall  not  interfere  with  the  view.  The  hand  should  rest 
lightly  on  the  table,  and  the  arm  should  not  to  any  extent 
participate  in  the  movement.  The  drawing  should  be 
made  by  the  hand  working  on  the  heel  as  a  pivot  and 
finishing  its  movement  at  the  wrist.  Do  not  attempt  to 
take  the  curve  farther  than  one  sweep  of  the  hand  will  carry, 
but,  having  reached  that  point,  move  the  hand  and  start 
afresh. 

Suppose  it  is  desired  to  draw  a  curved  line  as  a-b,  Fig.  3, 
some  guide  points  are  necessary  to  the  novice,  and  these 
may  simply  be  plotted  in  as  points,  through  which  it  is 
desired  the  curve  to  pass,  or  they  may  be  projected  from  a 
given  drawing,  such  as  points  in  the  plan  of  a  circular  sash, 
for  which  a  face  mould  is  required.  The  drawing,  then,  in 
its  preliminary  stage,  will  be  as  Fig.  I :  a',  i,  2,  b'  being  the 
points  the  curve  must  pass  through.  Next  put  in  a  series 


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130  TO    COPY    A    MOULDING 

of  dashes  or  points  between  the  main  ones  as  shown  by 
Fig.  2. 

The  middle  point  in  each  section  should  first  be  put  in  so 
that  the  general  appearance  of  the  curve  may  be  judged  ; 
having  obtained  these  satisfactorily,  put  in  others  as  close 
as  may  be  considered  necessary;  in  fact,  the  whole  curve  may 
be  dotted-in  this  way  without  much  departure  from  truth 
at  first  attempt,  but  if  correction  is  necessary,  it  is  easy  to 
erase  the  offending  dot.  Next  proceed  to  line-in  as  shown 
in  Fig.  4,  commencing  at  the  right  hand  and  joining  up  the 
dots,  not  by  short  steps,  but  by  a  bold  sweep  of  the  pencil, 
about  ij  in.  in  length.  If  a  few  "  trial  "  sweeps  are 
made  just  above  the  paper,  the  hand  will  get  into  the 
correct  swing. 

Probably  at  the  first  attempts  the  junctions  will  not 
flow  into  each  other  and  the  joints  will  be  plainly  seen,  but 
after  a  little  experience  it  will  be  possible  to  carry  the  hand 
forward  whilst  marking  the  line  and  so  get  a  firm,  continuous 
one  without  visible  junctions. 

To  copy  a  Moulding,  Fig.  6.— The  given  section  was 
drawn  mechanically — that  is,  with  rules  and  compasses — - 
but  the  copy  (Fig.  5)  is  entirely  freehand — i.e.  the  original 
of  this  print  was  so  drawn. 

It  is  shown  partly  finished  to  indicate  the  method  of 
procedure.  Draw  in  the  straight  lines  for  back  and  bottom 
of  the  moulding,  and  set  off  the  extremities  of  the  moulded 
part  as  shown  in  dotted  lines.  Next  draw  a  series  of  similar 
perpendicular  lines  on  each  drawing,  spacing  them  the  same 
distance  apart  in  each. 

Measure  the  height  of  each  upon  the  original  and  set  off 
heights  upon  the  copy ;  thus  a  series  of  points  will  be 
found  through  which  the  curve  may  be  drawn.  If  the  spaces 
are  too  wide  for  the  eye  to  carry  the  line,  dot  in  intermediate 
points,  as  advised  above.  You  may  or  may  not  use  instru- 
ments for  the  perpendiculars  and  measurements,  according 
to  the  degree  of  accuracy  required ;  it  is  quite  pedantic  to 
insist  on  every  construction  line  being  drawn  freehand. 


FREEHAND  131 

The  Cabinet  Screwdriver,  Figs.  7  and  8,  will  afford 
excellent  practice  in  "  balancing" — that  is,  making  the  op- 
posite parts  symmetrical  or  alike  on  each  side  of  a  centre 
line.  This  line  should  first  be  drawn,  then  horizontals  at 
various  points  of  chief  departure  in  the  curves,  and  dimen- 
sion points  marked  upon  them.  These  will  form  the  main 
guide  points,  and  others  can  be  placed  between,  until  suffi- 
cient are  obtained  to  complete  the  curves.  The  ends  of  the 
ferrule  are  curved,  to  convey  the  impression  of  roundness, 
which  is  further  suggested  by  the  shade  lines.  These  will  be 
referred  to  in  the  next  illustration,  Fig.  9,  which  is  a  Hollow 
Cylinder  or  pipe  as  viewed  when  standing  upright  just  below 
the  level  of  the  eye.  Draw  the  central  or  axis  line  joining 
the  centres  of  the  two  ends  ;  at  the  extremities,  draw  lines 
at  right  angles  to  the  axis.  These  will  be  the  diameters  of 
the  ends  and  the  correct  width  or  diameter  should  be 
ticked  off  thereon,  and  the  two  sides  of  the  cylinder  drawn. 
The  true  shape  of  the  cylinder  is  a  circle,  but,  as  stated  in  a 
previous  chapter,  a  circle  viewed  at  any  other  angle  than 
a  right  angle  to  its  plane  will  be  seen  as  an  ellipse,  the  minor 
axis  of  which  varies  as  the  angle.  We  need  not  trouble  to 
draw  this  axis  and  plot  the  curve  geometrically  as,  if  the 
drawing  is  approximately  correct,  it  will  convey  the  impres- 
sion intended.  Mark  a  series  of  points  equally  on  each  side 
of  the  diameter  lines  and  draw  in  the  curves ;  avoid  making 
the  ends  too  pointed,  and  make  the  lower  ellipse  slightly 
wider  than  the  upper,  as,  being  lower,  more  of  the  plane  can 
be  seen.  The  effect  of  roundness  is  given  by  drawing  a 
series  of  straight  lines  from  about  one-quarter  of  the  width 
to  the  edges,  gradually  increasing  their  distance  apart  as 
the  middle  is  approached.  This  gives  the  appearance  of 
light  upon  the  near  portion,  and  a  gradually  increasing 
shade  as  the  parts  recede. 

A  Stone  Baluster,  Fig.  10,  is  another  simple  exercise  in 
symmetrical  figures.  One-half  shows  the  preparatory  steps 
and  the  other  half  the  completed  drawing.  The  dotted  line 
drawn  parallel  with  the  centre  is  merely  a  convenience  for 


132  SQUARED    PAPER 

marking  the  dimensions.  The  central  line  should  first  be 
drawn,  and  then  the  various  horizontals  at  suitable  dis- 
tances ;  upon  these  the  widths  of  the  parts  should  be  ticked 
off  equally  on  each  side,  and  the  profile  of  the  turned  parts 
drawn  in. 

The  Screw  Wrench  (Fig.  n)  will  be  found  a  rather 
more  difficult  subject.  The  thread  of  the  screw  and  the  lines 
indicating  the  purfling  or  milling  of  the  thumb-nut  will 
test  the  student's  accuracy  in  drawing  parallel  lines  ;  the 
latter  should  be  drawn  closer  together  as  they  approach 
the  edges  to  give  the  effect  of  roundness.  Four  faint  lines 
should  be  drawn,  two  for  the  bottom  of  the  thread  and  two 
for  the  tops  or  outside,  and  after  the  threads  are  spaced  out 
and  drawn  across  at  a  slight  inclination,  the  intermediate 
parts  representing  stem  and  top  of  each  thread  should  be 
lined  in.  A  central  line  may  be  drawn  through  the  handle 
and  back  bar,  and  the  edges  set  off  equally  on  each  side 
and  the  jaws  drawn  perpendicular  to  it. 

The  Use  of  Squared  Paper,  or  the  ruling  of  lines  forming 
squares  upon  the  drawing,  is  a  device  that  will  be  found  of 
assistance  in  making  more  elaborate  freehand  drawings, 
such  as  the  masonry  details  shown  on  page  133  opposite ; 
also  for  enlarging  or  diminishing  a  drawing  proportionately. 
In  the  drawing  office,  tracing  paper  with  lines  ruled  in 
squares  of  suitable  dimensions  is  generally  used.  A  sheet 
is  secured  over  the  drawing  to  be  copied,  the  lines  that  are 
printed  on  it  breaking  the  drawing  up  into  a  number  of 
parts  with  location  points,  where  the  lines  intersect  the 
outlines  of  the  drawing.  If  the  drawing  is  to  be  copied  to 
the  same  size,  a  series  of  squares  of  similar  size  are  ruled  in 
pencil  over  the  drawing  paper,  and  the  various  points  ticked 
off  upon  it  just  as  they  occur  on  the  original.  Each  line  is 
numbered  similarly  on  both  sheets  to  assist  in  identifying 
the  points,  and,  when  a  sufficient  number  are  located,  the 
outline  can  be  completed  by  freehand. 

When  it  is  desired  to  enlarge  or  reduce  the  copy,  appro- 
priate size  squares  are  drawn  on  the  sheet  to  the  desired 


134  HINGES 

proportion.  Thus  in  the  drawing,  page  135,  the  carved 
spandrel  forming  part  of  the  window  head,  page  133,  is 
enlarged  to  treble  the  size  of  the  original,  and  if  it  were 
desired  to  reduce  it  to,  say,  one-third  the  size,  the  squares 
would  need  to  be  drawn  one-third  the  size  of  the  squares 
that  are  drawn  upon  the  original,  or  upon  the  tracing  paper 
used.  This  paper  is  procurable  at  the  drawing  instrument 
shops,  under  the  name  of  sectional  drawing  and  tracing 
paper,  and  it  can  be  obtained  ruled  in  squares  from  TV  in. 
to  ij  in.  The  smaller  rulings  on  drawing  paper  are  also 
used  for  making  drawings  to  scale  without  the  necessity 
of  using  "  scales " — e.g.  if  the  paper  is  ruled  in  i  in. 
squares  a  drawing  may  be  made  upon  it  to  scale  of  i  in. 
to  one  foot,  each  square  representing  one  foot,  and  a  line, 
say,  extending  over  six  squares  would  represent  6  ft.  and 
so  on. 

The  Series  of  Hinges  shown  on  page  137  will  afford 
good  exercise  in  freehand  drawing.  All  the  necessary  in- 
structions for  copying  are  embodied  in  the  previous  notes, 
but  a  brief  description  of  the  various  types  illustrated  may 
be  useful. 

The  Butt  Hinge,  Fig.  i,  page  137,  is  probably  the  com- 
monest ;  it  is  made  in  various  sizes  from  |  in.  to  6  in.  long, 
and  is  used  for  a  great  variety  of  purposes,  but  invariably 
upon  the -edges  of  the  parts  to  be  hinged;  thus  the  two 
"  edges  "  of  the  hinged  surfaces  come  together  when  closed 
and  are  said  to  "  abut  "  squarely  to  each  other,  hence  the 
generic  name  of  the  hinge,  distinguishing  it  from  the  types 
that  are  fixed  upon  the  surface  or  face  of  the  hinged  parts. 

The  flanges  or  wings  of  the  butt  are  always  sunk  in  flush, 
and  the  joint  or  "  knuckle  "  usually  projects,  that  the  door, 
etc.,  may  swing  clear  of  adjacent  projections,  but  in  some 
particular  cases  the  knuckle  is  sunk  flush  with  the  surface 
of  a  bead  on  the  edge  of  the  frame,  the  edge  of  the  door 
or  shutter  working  closely  around  the  bead.  This  method 
is  termed  by  joiners  "  close-joint  "  hanging.  The  details  of 
both  methods  are  fully  described  in  the  author's  work  on 


136  BAGATELLE    STRAPS 

Practical  Joinery.  Butt  hinges  are  made  of  cast-steel, 
wrought-iron,  cast  and  rolled  brass  and  gun-metal. 

The  Projecting  Butt,  Fig.  2,  is  made  much  wider  than 
the  average,  and  the  projecting  portions  are  thickened  to 
improve  the  appearance.  They  are  used  where  there  is  some 
large  moulding  or  other  projecting  part  adjacent  to  the 
door  which  it  is  required  to  fold  upon.  The  example  shown 
is  further  strengthened  by  hardened  steel  bushes  upon  the 
working  surface,  the  remaining  portion  of  the  hinge  being 
usually  brass  or  gun  metal. 

The  Back  Flap,  Fig.  3,  though  of  somewhat  the  same 
appearance  as  the  butt,  belongs  to  the  surface  type.  It  is 
chiefly  used  upon  shutters  or  similar  objects  which  are  not 
sufficiently  thick  to  accommodate  butt  hinges  upon  their 
edges.  Some  fastidious  people  require  it  sunk  flush  with 
the  surface,  but  strength  is  thus  sacrificed  to  appearance. 
The  wings  taper  as  shown  in  the  plan,  and  they  are  always 
wider  than  long.  They  obtained  their  name  because 
originally  they  were  made  for  the  back,  or  inner  flaps  of 
boxing  shutters,  butt  hinges  being  used  on  the  front  flap, 
which  was  made  thicker  to  provide  sunk  panels. 

The  Table  Hinge,  Fig.  16,  is  a  special  form  of  back 
flap  used  in  hinging  the  flaps  or  leaves  of  tables.  The  two 
points  of  difference  are,  that  the  joint  is  so  formed  that  the 
wings  will  open  back  square  to  each  other,  consequently 
the  knuckle  projects  upon  the  back  surface  instead  of  the 
front  or  countersunk  side,  which  is  sunk  flush  with  the  table 
top,  thus  allowing  the  brackets  to  pass  freely  underneath. 
The  wings  are  of  different  length,  or  rather  width ;  this  is 
necessary  because  one  has  to  bridge  the  hollow  in  the  edge 
of  the  flap  as  shown  in  the  sketch. 

The  Bagatelle  Strap  or  Desk  Hinge,  Fig.  4,  is  a  small 
brass  hinge  of  the  butt  type,  with  wings  abnormally  wide 
in  comparison  to  their  length.  They  are  used  upon  narrow 
margins  to  openings,  such  as  desk  flaps,  bagatelle  table 
covers  and  the  like,  are  made  of  cast-brass,  and  in  sizes  from 
i  in.  x  yV  in.  to  2j  in.  x  y|-  in. 


•g. 

C/2 

10 
C 

rt 

I 

2 


138  MISCELLANEOUS    HINGES 

The  Rising  or  Helical  Butt,  Fig.  5,  is  generally  made  of 
polished  brass,  with  hard  steel  bearings.  They  vary  in  size 
from  3  in.  to  6  in.  long,  and  are  used  for  doors  that  have 
to  pass  over  thick  carpets,  lifting  the  door  about  fth  in., 
when  it  is  full  open.  Of  course  the  door  will  not  open  so 
far  back  as  the  hinge  is  shown  in  the  drawing  ;  these  butts 
are  made  "  handed."  The  one  shown  is  for  a  left-hand 
door — -i.e.  a  door  hung  with  the  lock  to  shoot  towards  the 
left  hand  of  the  person  viewing  the  face  of  the  door. 

The  Trestle  Hinge,  Fig.  6,  used  for  hinging  builders 
"  trestles "  or  scaffold  steps,  is  made  in  wrought  and 
malleable  iron  in  sizes  from  6  in.  to  14  in.  They  are  fixed 
upon  the  surface  of  the  frames  and  are  of  the  strap  type. 

The  Parliament  or  Shutter  Hinge,  Fig.  7,  has  extended 
wings  and  narrow  side  straps  for  the  purpose  of  fixing  them 
to  the  edges  of  frames.  They  are  of  the  butt  type,  and  are 
used  for  shutters  that  have  to  fold  back  on  the  face  of  a 
wall.  The  projection  of  the  knuckle  must  equal  half  the 
depth  of  the  reveal  of  the  opening  into  which  the  frame  is 
sunk.  The  hinge  is  said  to  have  obtained  its  name  because 
it  was  introduced  to  comply  with  an  Act  of  Parliament 
requiring  that  doors  and  shutters  opening  upon  footways 
should  be  folded  back  upon  the  walls.  They  are  made  in 
sizes  4  in.,  4^  in.,  5  in.  and  6  in.,  measured  as  shown  in  Fig.  7. 

The  Pew  Hinge,  Fig.  70,  is  a  variation  of  the  shutter 
hinge,  having  an  egg-shaped  joint,  used,  as  its  name  implies, 
for  pew  and  similar  shaped  doors. 

The  Counter  Flap  Hinge,  Fig.  8,  also  known  as  a  link 
hinge,  when  made  in  iron  and  of  large  size,  for  cellar  flaps, 
is  chiefly  used  for  flaps  in  counter  tops,  the  object  of  the 
link  being  to  allow  the  flap  to  lie  back  flat  on  the  counter 
without  the  necessity  of  having  a  projecting  knuckle.  As 
will  be  seen  by  the  edge  view,  it  is  sunk  flush  with  the  top 
surface,  and  it  is  made  of  dovetailed  shape  to  resist  side 
pressure.  Obtainable  in  cast-brass,  gun-metal  and  nickelled 
steel.  Sizes  from  ij  in.  to  2j  in. 

Strap  Hinges. — This  term  is  applied  in  the  ironmongery 


GATE    HINGES  139 

trade  to  that  class  of  hinge  which  fixes  upon  the  face  of  the 
door,  etc.,  and  that  is  in  two  parts — -that  is,  the  axis  or 
pivot  upon  which  the  hinge  works  is  made,  and  is  attached 
separately  to  the  post  or  frame,  and  the  band  or  strap,  after 
securing  to  the  door,  is  lifted  upon  the  pivot.  There  are 
two  distinct  types — -viz.  single  and  double  straps,  and  several 
varieties  of  each. 

The  Hook  and  Eye  Hinge,  Figs.  9  and  ga,  is  a  common 
form  of  single  strap  hinge  used  for  stable  doors,  etc.,  having 
to  swing  clear  of  obstacles  at  the  bottom.  It  will  reverse 
and  the  door  can  be  readily  lifted  off  the  hook  or  pivot. 
Made  in  wrought-iron  in  sizes  from  18  in.  to  36  in.,  in- 
creasing 2  in.  The  one  shown  is  drilled  for  bolts,  but  they 
can  be  obtained  countersunk  for  screws. 

The  "Park-Gate"  or  "Collinge"  Hinge,  Figs.  10 
and  n,  is  a  typical  double  strap  and  spur  hinge,  used,  as  the 
name  implies,  for  large  entrance  gates  to  gardens  and  parks. 
The  hinge  shown  is  the  top  one,  and  is  for  a  right-hand-hung 
gate  ;  the  lower  hinge  has  no  strap,  merely  a  spur,  and  may 
work  upon  a  centre  pivot  as  at  top,  or,  as  is  more  usual, 
upon  two  pivots  placed  side  by  side  about  3  in.  apart  to 
throw  the  gate  up  as  it  opens,  to  clear  the  rise  in  the  road- 
way. 

Collinge  is  the  name  of  the  inventor.  The  hinges  are  to 
be  obtained  from  2  ft.  to  6  ft.  long  and  to  suit  any  thickness 
of  gate. 

The  Egg  and  Cup  Hinge,  Figs.  12  and  13,  is  a  single 
strap,  and  is  used  for  coach-house  and  similar  "  close " 
doors.  The  strap  is  fitted  with  a  ball  or  egg-shaped  bearing, 
ground  to  fit  a  cup  attached  to  the  hanging  plate.  It  is 
also  provided  with  a  cover  or  hood,  which  protects  the  bear- 
ings from  dirt.  Different  shaped  cup-holders  are  used 
upon  wood,  stone  and  brick  piers.  Fig.  13  shows  the  shape 
for  a  wood  post  and  Fig.  14  for  a  stone  pier.  The  one  used 
in  brickwork  is  forked,  with  the  ends  turned  up  and  down. 

The  Cross  Garnet,  Fig.  15,  known  also  as  a  T-hinge,  is 
a  common  form  of  strap  for  light  doors  and  gates.  It  is 


140  SPRING   HINGES 

made  in  malleable  and  wrought-iron  in  sizes  from  6  in.  to 
24  in.  long.  The  form  of  joint  shown  in  Fig.  i$a  is  called 
a  water  joint. 

The  Floor  Spring  Hinge,  Figs.  17  to  19,  is,  so  far 
as  its  hinging  property  is  concerned,  merely  a  pivot  hinge, 
but  the  lower  pivot  in  this  instance  is  connected  to  a  shoe 
which  carries  the  door,  and  to  helical  spring  or  springs 
(according  to  the  make)  contained  in  a  metal  box  concealed 
in  the  floor.  The  object  of  the  springs  is  to  cause  the  door 
to  close  automatically.  The  shoe  is  usually  arranged  to 
swing  both  ways,  and  for  that  reason  it  is  frequently  called 
a  swing-door  hinge.  The  sizes  vary  with  different  makers, 
but  the  dimensions  shown  are  average. 

The  top  or  visible  plate  is  of  brass,  also  the  shoe,  the 
remaining  parts  being  of  steel.  As  the  doors  must  be  fitted 
into  the  shoe,  then  into  the  opening  exactly,  the  top  pivot 
requires  insertion  after  the  door  is  in  position. 

The  usual  arrangement  is  shown  in  Fig.  18,  where  the 
plate  A  is  fixed  into  the  head  of  the  door  ;  the  plate  B  into 
the  frame  with  the  lever  concealed  in  its  thickness. 

When  the  door  is  in  position,  the  screw  shown  on  the  right 
hand  is  turned  up,  carrying  the  other  end  of  the  level  down 
when  the  pin  enters  the  socket  and  fixes  the  door.  With 
thin  or  high  doors  it  is  necessary  to  have  a  hinge  in  the 
middle,  to  prevent  their  casting  ;  the  usual  form  is  shown 
in  Fig.  19. 


CHAPTER   X 
PRACTICAL    GEOMETRY 

Bevels  and  Angles  in  Oblique  Planes.  Simple  Angles.  Com- 
pound Angles — rotation  of  inclined  plane.  Cuts  for  Purlins 
against  Hips.  Oblique  Cuts  in  Angle  Braces — various  positions 
of  brace,  development  of  inclined  surfaces.  Bevels  in  Splayed 
Linings — setting  out  the  soffit.  Properties  of  and  methods  of 
drawing  Ellipses — definition  of  ellipse  and  terms  connected  with 
same.  Sections  of  Cylinders.  Describing  Ellipse  by  intersect- 
ing lines,  ditto  by  Trammelling.  To  find  the  Foci,  Normal  and 
Tangent  of  an  Ellipse.  False  Ellipses.  The  Cone  and  its 
Properties — definitions,  projections.  The  Conic  Sections — how 
to  produce  them.  The  Covering  of  Cones.  Development  of 
Frustum  of  Cone.  The  Covering  of  Domes  and  Vaults — types 
of  Domes.  To  obtain  projection  of  boarding.  To  obtain  Shape 
of  boards  laid  vertically ;  ditto  laid  horizontally.  A  Gothic 
Dome — to  project  the  ribs.  An  Elliptic  Dome — to  obtain  the 
covering  of.  Setting  out  Arches  in  Brick  and  Stone — the  gauged 
camber,  round,  elliptic,  lancet,  equilateral,  Tudor,  horseshoe, 
stilted,  basket  handle,  ogee  and  squinch  arches.  Carpentry 
Arches — Gothic,  method  of  finding  centres  for.  The  Wave,  Ogee 
and  Bell  Arches.  Complex  Curves.  The  Helix — methods  of 
drawing.  "  Pitch  "  explained.  Development  of  Helical  Curve. 
Projecting  a  Wreathed  Handrail.  The  Spiral — definition.  To 
draw  the  rising  Spiral,  the  Plane  Spiral.  Drawing  Scrolls 

The  Determination  of  Bevels  and  Angles  in  Oblique 
Planes. — This  is  a  class  of  problem  which  in  one  form 
or  another  is  constantly  occurring  in  the  workshop  and  draw- 
ing office.  The  carpenter  meets  with  it  in  variety  in  framing 
up  a  roof  ;  the  joiner  when  fitting  the  mitres  of  splayed 
linings  or  joints  of  curved  and  splayed  fascias,  etc.;  the  . 
bricklayer  and  the  mason  in  preparing  templets  for  splayed 
and  skew  arches  or  in  the  angles  of  window  and  door 
openings ;  the  plumber  when  obtaining  shapes  of  lacing 
141 


142  SIMPLE    ANGLES 

sheets  for  turret  roofs,  etc.  The  reader  who  has  followed 
the  chapter  on  orthographic  projection  will  scarcely  need 
telling  that  a  drawing  of  an  angular  or  any  other  shaped 
plane  surface  gives  the  true  size  and  shape  of  that  surface 
only  when  projected  upon  a  plane  parallel  with  itself. 

In  most  technical  drawings  in  which  oblique  surfaces 
occur,  however,  these  will  be  found  projected  upon  a  plane 
not  parallel  with  the  oblique  surface,  and  to  obtain  either 
the  real  shape  and  dimensions  or  the  true  angles  at  the  in- 
tersections special  projections  must  be  made,  and  it  is  with 
these  we  now  deal.  To  make  the  matter  quite  clear  as  to 
when  a  special  drawing  or  development  is  required,  a  few 
examples  of  intersecting  surfaces  at  various  angles  which 
do  not  require  special  treatment  are  first  given  (see  page 

143); 

Simple  Angles. — Figs,  i  and  2  show  two  pieces  of 
wood  at  right  angles  to  each  other,  and  it  is  obvious  that 
the  square  applied  as  shown  will  give  the  correct  cut  for  the 
joint.  Again,  in  Figs.  3  and  4  we  have  the  piece  B  fitted 
against  the  piece  A ,  and  as  it  lies  horizontal  in  one  direction 
its  true  shape  is  shown  in  the  plan  and  a  "  square  "  gives  the 
joint.  The  piece  B  is  inclined  in  the  other  direction,  conse- 
quently the  view  at  right  angles  to  the  plan  will  show  its 
true  inclination,  and  the  edge  bevel  is  obtained  as  shown  in 
Fig.  4.  If  piece  B  is  level  and  piece  A  vertical,  but  making 
any  angle  with  B  in  plan,  then  the  true  bevel  is  shown  in 
the  plan  as  at  Fig.  6,  and  obviously  the  depth  of  the  cut  is 
square.  Other  simple  angles  are  shown  on  page  146,  on 
the  left  side  of  Figs,  i  and  2,  and  on  Fig.  4. 

Compound  Angles. — These  arise  when  one  or  both  of 
the  intersecting  surfaces  are  at  angles  other  than  right 
angles — that  is,  square  to  each  other — and  one  or  both  of 
the  surfaces  are  inclined  in  transverse  direction.  Such  cases 
occur  in  splayed  linings  or  jambs,  in  hipped  roofs,  in  angle 
braces,  hoppers,  etc.,  and  the  method  of  development  now 
to  be  described  will  disclose  the  bevels  or  "  cuts  "  required 
in  all  such  cases. 


COMPOUND    ANGLES 


143 


Figs.   7,   8    and   9   show   a   horizontal    board    inclined 
at  30°  across  its  width,  fitting  against  a  vertical  board, 


.0,Z- 


SJ    4 

I 


standing  at  an  angle  of  45°  in  plan.     The  shoulder  cut  a-l 
is  required.     A  glance  at  Figs.  7  and  9,  the  plan  and  eleva- 


144  OBTAINING    OBLIQUE    CUTS 

tion,  which  are  the  usual  drawings  given,  will  show  that 
the  true  length  of  the  line  required,  a'-b,  is  not  shown  in 
either  drawing.  If,  however,  we  conceive  the  edge  a  lifted 
up  until  it  is  level  with  b,  the  point  b  remaining  fixed,  we 
should  then  have  the  surface  parallel  with  the  plan,  and, 
drawn  thus,  its  true  shape  would  be  disclosed. 

To  do  this,  set  off.  on  Fig.  7,  the  real  width  of  the  piece  B, 
obtained  at  a-~by  Fig.  9,  and  draw  the  developed  edge  parallel 
to  its  original  position,  a-^a-r.  Intersect  this  line  at  a'  by  a 
projector  perpendicular  to  it,  from  point  a  ;  this  locates 
point  a  in  its  new  position,  and  as  point  b  has  not  moved, 
if  we  join  a'-b,  obviously  we  obtain  the  true  shape  of  the 
bevel  or  cut  to  fit  against  the  piece  A. 

In  Figs.  10  to  12  are  shown  a  plan  and  two  elevations  of 
a  vertical  piece  A,  standing  at  an  angle  of  58°  with  the  edge 
of  its  base,  and  a  doubly  inclined  piece  B,  fitting  against  it ; 
the  oblique  cuts  a-b  and  c-d  are  required.  To  obtain  these 
a  similar  method  is  pursued.  It  may  be  well  to  describe  first 
the  method  of  making  the  orthographic  projections.  The 
essential  data  are  :  the  width  of  base  is  14  in. ;  angle  between 
vertical  piece  and  edge  of  base,  58°  ;  angle  between  base  and 
brace  or  inclined  piece,  40° ;  height  of  top  of  brace,  2  ft. ; 
front  edge  of  brace  to  be  5  in.  lower  than  back  edge.  Pro- 
ceed to  draw  Figs.  10  and  12  to  these  conditions,  then  project 
the  elevation  Fig.  n  from  them,  as  indicated  by  the  dotted 
projectors.  Having  found  position  of  point  a  in  Fig.  n, 
draw  the  front  edge  of  B  at  the  required  angle  from  it  and 
the  back  edge  parallel  thereto.  Next  project  points  c  and 
d  into  the  plan,  and  draw  the  joint  c"-dr.  This  completes 
the  projections  and  we  can  proceed  with  the  developments. 

The  first  thing  required  is  the  true  width  of  piece  B,  which 
neither  of  the  projections  show.  To  obtain  this,  turn  the 
piece  A  into  the  vertical  plane  by  taking  point  b"  as  centre 
and  a"-b"  as  radius ;  describe  the  arc  a"-a2,  then  project  this 
point  into  the  vertical  plane  as  shown,  and  intersect  it  at 
a3  by  a  horizontal  projector  from  point  a.  Join  a3-b',  and 
the  real  length  of  the  line  a-bf  is  seen.  Set  off  this  length 


PURLIN    CUTS  145 

upon  a  perpendicular  to  the  edge  b'-d  drawn  from  b' '.  Draw 
a  parallel  to  b'-d  through  this  point  and  the  true  width  of  B 
will  be  obtained.  Next  we  locate  upon  it  points  e  and  /,  by 
projecting  perpendiculars  from  points  a  and  c.  Join  these 
points  to  br  and  d  respectively,  and  the  true  size  and  shape  of 
the  angle  piece  is  obtained  with  the  bevels  as  shown. 

To  obtain  the  Cuts  for  Purlins  against  Hips.— Figs. 
13  and  14  are  the  plan  and  elevation  of  the  angle  of  a 
hipped  roof  showing  the  ends  of  the  purlins  fitting  against 
the  hip  rafter.  These  are  the  usual  projections  given,  from 
which  we  obtain  the  bevels  by  developing  the  inclined 
surfaces  of  the  purlin  into  a  horizontal  plane. 

With  point  c  in  Fig.  14  (the  top  edge  of  the  purlin)  as 
centre,  and  the  widths  of  the  edge  and  side  as  radii,  describe 
arcs  cutting  the  horizontal  line  in  points  a'  and  b'.  Drop 
projectors  from  these  points  into  the  plan  and  intersect  them 
by  perpendiculars  from  the  edges  of  the  purlin,  where  they 
come  in  contact  with  the  hip,  thus  obtaining  points  a*-bz ; 
join  these  to  point  c'  and  the  bevels  are  disclosed. 

Oblique  Cuts  in  Angle  Braces. — Figs,  i  and  2,  page 
146,  are  the  plan  and  elevation  respectively  of  a  post 
or  standard  resting  upon  a  sole  piece  and  counter  braced. 
To  utilise  the  space  fully,  different  arrangements  of  the 
braces  are  shown  on  either  side,  but  in  practice  they  would 
be  alike  on  each  side.  The  brace  on  the  left  side,  as  will 
be  seen  by  its  plan,  lies  parallel  to  the  plane  it  is  drawn  upon, 
therefore  all  its  edges  are  shown  in  actual  length  and  position 
and  the  bevels  are  obtainable  directly  from  the  drawing. 

Upon  the  right-hand  side  the  brace  is  shown  with  one  of  its 
diagonals  vertical,  or,  stated  otherwise,  it  lies  with  its  arris 
edges  in  a  vertical  plane  ;  this  can  be  better  seen  in  the  side 
elevation,  Fig.  3.  A  bevel  set  to  the  projection  would  give 
the  correct  shape  for  the  housing  into  the  post,  but  not  the 
bevel  to  apply  to  the  sloping  sides  of  the  brace  for  marking 
the  shoulder  cuts.  These  must  be  obtained  by  developing 
the  sloping  surfaces  or  turning  them  into  the  vertical  plane. 
Perhaps  it  would  be  clearer  to  say  that  the  two  edges  must 


Fig  2 


Fig.1. 


Fi(f.6.  : 


b' 


Fw.5. 


Obtaining  Bevels  upon  Oblique  Planes 


BEVELS    ON    OBLIQUE    PLANES  147 

be  brought  into  one  plane  ;  it  does  not  really  matter  which 
plane  it  is.  As  it  may  not  be  clear  how  the  elevation  of 
the  brace  is  obtained,  this  will  be  first  described. 

Draw  the  line  a-b,  Fig.  2,  at  the  pitch  the  brace  is  desired, 
and  the  line  1-2  perpendicular  to  this  ;  upon  this  set  off  the 
half-diagonal  of  the  given  brace  on  either  side,  obtaining 
the  dimension  from  a  drawing  or  the  stuff  itself.  Draw 
parallels  to  a-b  through  1-2,  which  will  give  the  projections 
of  the  upper  arid  lower  edges. 

The  section  of  the  brace  is  dotted-in  to  make  the  explana- 
tion clearer  ;  this  is  drawn  by  setting  off  the  transverse 
diagonal  and  joining  up  the  corners  1-2-3-4.  Next  draw 
a  line  square  to  the  pitch  through  the  lower  corner  and  turn 
the  sides  down  upon  it.  Draw  parallels  to  the  edges  through 
these  points  and  intersect  them  by  perpendiculars  drawn 
from  each  end  of  the  brace  as  at  c~d.  Join  the  points  so 
obtained  to  points  a  and  b,  and  the  bevels  will  be  found. 

A  similar  post  is  shown  in  Figs.  5  and  6.  Here  the  post 
is  so  placed  that  the  braces  pitch  against  its  diagonal. 

The  same  method  is  used  to  obtain  the  bevels  for  the  right- 
hand  brace,  which  should  offer  no  difficulty  to  the  student, 
although  the  bevels  obtained  differ  from  the  last  set.  The 
braces  being  square  in  section,  both  cuts  are  really  alike,  and 
the  development  of  the  undersides  is  unnecessary,  but  both 
are  shown  to  make  the  method  clear. 

If  the  brace  were  at  an  angle  of  45°  only  one  bevel  would  be 
necessary,  as  each  end  would  be  alike.  On  the  left  side  of 
Fig.  5  the  brace  is  shown  with  its  sides  parallel  to  the  vertical 
plane,  consequently  the  down  cut  and  foot  cut  are  shown 
correctly  in  the  elevation.  Two  methods  of  obtaining  the 
edge  cut  or  bird's-mouth  are  shown.  First  the  point  e  may 
be  thrown  down  level  with  x,  the  lowest  point  in  the  bird's- 
mouth,  and  projected  into  the  plan,  where  it  is  intersected 
at  e"  by  the  side  h"  produced.  Join  &"-%'  and  the  true  shape 
of  the  bird's-mouth  is  seen.  Second,  a  development  of  upper 
side  of  brace  may  be  made  on  the  elevation,  projecting  across 
it  the  point  x  to  the  middle,  where  it  meets  the  angle  of  the 


148  SPLAYED    LININGS 

post.  Join  this  point  to  e~e'  and  a  templet  for  marking  the 
brace  is  obtained. 

In  Fig.  7  a  development  of  the  two  adjacent  sides  of  the 
post  is  made,  chiefly  to  show  the  limits  within  which  the 
mortise  and  tenon  must  be  made  ;  also  how  to  mark 
the  housing.  The  bevels  are  the  same  as  those  found  for 
the  brace,  but  are  applied  in  reverse  direction.  The  dis- 
tance of  point  a  from  c  is  found  in  the  plan  ;  the  heights 
of  the  points  are  projected  from  Fig.  5. 

Obtaining  the  Bevels  of  Splayed  Linings. — An  open- 
ing fitted  with  a  French  casement  frame,  having  splayed 
linings  to  jambs  and  soffit,  is  shown  on  page  149.  One- 
half  of  plan  and  elevation  is  shown  in  detail,  the  other  half 
in  line  diagram,  showing  the  developments  necessary  to 
determine  the  true  angles  at  the  mitre,  to  obtain  the  bevels 
for  marking  the  shoulders.  The  soffit  is  splayed  at  a  less 
angle  than  the  jambs,  the  usual  method,  as  the  splay  is 
given  only  for  effect,  it  is  not  necessary  to  obtain  light  ; 
the  rays  of  light  pass  downwards  not  upwards,  and  the 
ceiling  is  lighted  by  reflection  from  the  surfaces  in  the  room. 
If  the  splays  were  alike,  only  one  bevel  would  be  required. 
The  mitre  line  a'-b2,  shown  at  top  of  Fig.  3,  is  the  projection 
of  the  angle,  and  is  not  its  real  length  or  inclination.  To 
obtain  this  we  must  turn  the  lining  round  parallel  to  the 
front.  Let  a,  Fig.  i,  be  the  pivot,  move  b,  the  outer  edge  of 
the  lining,  round  to  b' ;  the  edges  represented  by  a  and  b 
will  then  be  in  one  plane.  Referring  to  the  elevation,  point 
a'  will  not  have  moved  in  the  operation,  point  b2  has  moved 
out  horizontally  to  b"r,  which  is  the  point  where  the  two  pro- 
jectors meet.  Join  this  point  to  a'  and  we  have  the  shoulder 
line  for  the  jamb.  To  obtain  the  bevel  for  the  soffit. 
In  like  manner  upon  section  Fig.  4,  with  a  as  centre  and 
a-b*  as  radius,  describe  an  arc  intersecting  the  vertical  plane 
in  b*.  Project  this  point  into  the  elevation,  cutting  the 
projector  from  the  face  of  the  jamb  in  b"". 

Join  this  point  to  a'  and  the  bevel  for  the  head  groove 
is  disclosed. 


Obtaining  Bevels  in  Splayed  Linings 

Fig.  i.  Plan  of  French  Casement  Window.  Fig.  2.  Half  Elevation  of 
Sam.i.  Fij.  3.  Development  of  Linings.  Fig.  4.  Vertical  Section  of 
Window 


ISO  ELLIPSES 

The  soffit  would  be  laid  upon  the  rod  and  point  a'  marked 
on  each  side,  then  the  bevel  just  found  applied  to  front  edge 
with  blade  intersecting  point  a',  and  the  line  cut  in.  A 
second  line  about  f  in.  farther  out  and  parallel  with  the  first, 
would  be  added  to  mark  the  groove  for  the  reception  of  the 
tongue  which  is  cut  upon  end  of  the  jamb. 

The  bevel  found  for  the  jamb  would  be  applied  at  the 
back  to  mark  the  shoulder,  the  tongue  being  formed  on  the 
face  side,  as  shown  in  the  plan. 

Properties  of  and  Methods  of  drawing  Ellipses.— 
The  ellipse  is  a  figure  used  almost  as  frequently  as  the 
circle  by  the  architectural  draughtsman,  and  its  construction 
is  constantly  required  in  the  workshop.  There  is  a  consider- 
able amount  of  misconception  concerning  this  figure  ;  it 
is  often  confounded  with  other  figures  to  which  it  has  no 
relation,  for  instance  the  oval  and  the  three-centred  circular 
curve. 

Definitions. — The  Ellipse  is  a  section  of  either  a  cone  or 
a  cylinder.  It  may  be  defined  as  a  plane  figure  bounded  by 
one  continuous  curve  described  about  two  points  (called  the 
foci),  so  that  the  sum  of  the  distances  from  any  point  in  the 
curve  to  the  two  foci  may  be  always  the  same  (see  Fig. 
7,  page  152). 

Axes. — A  diameter  of  an  ellipse  is  any  straight  line 
cutting  it  in  halves  by  passing  through  its  centre.  One 
diameter  is  conjugate  to  another  when  it  is  parallel  to  the 
tangents  passing  through  the  ends  of  the  other.  The  longest 
and  shortest  conjugate  diameters  are  at  right  angles  with 
each  other,  and  as  the  figure  is  symmetrical  about  them,  they 
may  be  called  axes,  and  they  are  generally  called  the  major 
(or  greater)  and  minor  (or  lesser)  axes  respectively.  The 
point  of  intersection  of  the  two  axes  is  called  the  centre  of 
the  ellipse,  and  the  axis  of  the  generating  cylinder  (or  cone) 
always  passes  through  this  point. 

Ordinates  are  lines  drawn  from  the  circumference 
perpendicular  to  the  axis  or  diameter  (see  Figs,  i  and  2). 

Foci. — Two  points  on  the  major  axis,  from  which  the 


DRAWING    ELLIPSES  151 

curve  has  a  constant  ratio — that  is,  the  sum  of  the  distance 
of  any  point  in  the  curve  from  the  two  focal  points  is  equal 
to  the  length  of  the  major  axis  ;  this  will  be  demonstrated 
in  reference  to  Fig.  7. 

Normals  are  lines  perpendicular  to  the  curve  at  any 
particular  point. 

Tangents  are  lines  at  right  angles  to  the  normal  and 
touching  the  curve. 

Trammel. — An  apparatus  or  instrument  for  describing 
elliptic  curves  mechanically. 

Trammelling'. — A  method  of  plotting  an  ellipse  upon 
its  axes  similar  in  principle  to  the  action  of  the  trammel. 

Methods  of  drawing  the  Ellipse. — There  are  many 
methods  of  doing  this,  several  of  which  are  shown  on  page 
152.  First  as  the  section  of  a  cylinder.  Let  a-b-c-d, 
Fig.  i,  be  the  elevation  of  a  cylinder,  whose  plan  is  shown 
in  Fig.  2.  To  obtain  the  section  made  by  a  plane  on  the 
line  A-A,  divide  the  semi-circumference  of  the  plan  into  a 
number  of  equal  parts,  as  i,  2,  3,  4,  5,  6,  7,  8  ;  project  these 
points  to  the  line  of  section  as  shown  by  the  dotted  pro- 
jectors, numbering  them  similarly  for  easy  reference.  Erect 
perpendiculars  to  the  line  of  section  from  these  points,  and 
make  them  equal  in  length  to  the  corresponding  ordinates 
in  plan.  Draw  the  curve  through  the  points  so  found. 
Another  plane  of  section  is  shown  by  the  line  B-B,  and  the 
complete  section  is  described  on  a  line  parallel  to  the  line  of 
section,  but  clear  of  the  generating  solid.  The  same  pro- 
jectors are  utilised  as  in  the  first  case,  the  only  difference 
in  treatment  being  that  the  lengths  of  the  ordinates  are  set 
off  on  each  side  of  the  central  line  or  major  axis,  0-8. 

To  Describe  a  Semi-Ellipse  by  means  of  intersecting 
lines,  Fig.  3. — Draw  a  rectangle  upon  the  major  axis  equal 
in  height  to  the  minor  axis,  as  a~b,  b-a.  Divide  each  side 
into  the  same  number  of  equal  parts  as  shown  ;  join  points 
fl-i,  1-2,  2-3,  3-c,  etc.,  and  through  the  points  where  these 
lines  intersect  each  other,  draw  the  curve.  If  a  sufficient 
number  of  divisions  are  used  the  curve  will  be  described  by 


TRAMMELLING  153 

the  intersecting  lines,  all  of  which  are  tangents,  and  each 
one  produces  a  point  in  the  curve. 

To  Describe  the  Ellipse  by  Trammelling,  Fig.  4. — 
Draw  the  major  and  minor  axes  perpendicular  to  each  other. 
Take  a  strip  of  paper  or  wood  and  mark  off  from  one  end 
the  lengths  of  the  semi-major  and  semi-minor  axes  respect- 
ively, as  shown  at  M1,  M2.  If  now  the  strip  is  placed  across 
the  axes  so  that  these  points  rest  on  them  as  shown  in  two 
positions  in  Fig.  4,  the  end  of  the  rod  will  be  in  the  curve  at 
that  particular  point,  and  if  it  is  marked  with  a  pencil  a 
sufficient  number  of  such  points  maybe  found,  through  which 
the  curve  may  be  drawn  either  freehand  or  by  aid  of  wood 
curves.  This  method  is  especially  useful  in  producing  small 
ellipses  in  which  the  trammel  itself  is  rather  cumbersome. 

Another  method  of  drawing  an  ellipse  by  means  of  inter- 
secting lines  is  shown  in  Fig.  8,  and  it  is,  perhaps,  the  clearest 
and  best  for  draughtsmen.  Draw  the  major  axis  A-B,  and 
the  semi-minor  axis  x-c  perpendicular  to  it.  Describe  two 
circles,  one  on  the  major  axis,  the  other  on  the  minor  (one- 
half  only  is  shown).  Divide  each  semicircle  into  the  same 
number  of  equal  parts,  and  this  is  best  done  by  drawing 
radials  from  the  centre  to  the  divisions  on  the  large  circle  ; 
these  will  divide  the  smaller  one  similarly,  as  shown  by  the 
dotted  lines  in  the  left  quadrant.  From  the  points  on  the 
outer  circle  draw  ordinates  parallel  with  the  minor  axis,  and 
from  the  corresponding  points  on  the  inner  circle  draw  lines 
parallel  to  the  major  axis.  The  intersections  of  these  lines 
will  be  points  in  the  elliptic  curve,  which  may  then  be  drawn 
through  them. 

To  find  the  Centre  and  Axes  of  a  given  Ellipse.— Let 
M-M,  m-m,  Fig.  5,  be  the  given  ellipse  ;  draw  any  two  lines 
parallel  and  cutting  opposite  sides  of  the  ellipse,  as  A~A 
and  B-B.  Bisect  each  of  these  and  draw  the  line  D-D 
through  their  centres.  Bisect  D-D  in  point  C,  which  is  the 
centre  of  the  ellipse.  To  determine  the  direction  of  the 
axes.  With  C  as  centre,  and  any  radius,  describe  a  circle 
cutting  the  ellipse  in  points  1-2-3.  J°in  1-2  and  2-3,  and 


154  FINDING    NORMALS 

lines  drawn  parallel  to  these  through  the  centre  will  be  the 
major  and  minor  axis  respectively. 

To  find  the  foci,  normal  and  tangent,  of  any  ellipse  (see 
Fig.  6).  With  the  semi-major  axis  as  radius  and  either  end 
of  the  minor  axis  as  centre,  describe  an  arc  cutting  the  major 
axis  in  F.F.  These  are  the  two  focal  points. 

Normals. — Let  n,  Fig.  6,  be  a  point  in  the  curve  to  which 
we  desire  to  find  a  normal  or  perpendicular.  From  this  point 
draw  lines  to  the  foci  F-F.,  and  bisect  the  angle  contained 
between  them.  This  is  done  by  describing  an  arc  from  point 
n,  and  from  the  ends  of  the  arc,  with  same  radius,  describe 
intersecting  arcs.  Draw  a  line  through  this  point  and  the 
given  point  n.  This  line  is  normal  to  the  curve  at  that 
particular  point,  and  any  other  may  be  found  in  like 
manner.  This  method  is  used  to  obtain  the  joint  lines  of 
the  voussoirs  in  elliptic  arches,  and  for  the  ribs  of  centering. 

A  tangent  at  the  same  point  is  readily  found  by  drawing 
a  line  at  right  angles  to  the  normal  and  touching  the  curve. 

To  describe  an  Ellipse  by  Means  of  a  Looped  String, 
Fig.  7. — Draw  the  conjugate  axes  to  dimensions  required, 
and  find  the  focal  points  as  described  in  Fig.  6.  Drive  two 
pins  in  the  foci,  as  at  1-2,  and  a  third  pin  at  A,  one  end  of 
the  major  axis.  Form  a  tight  loop  with  thread  or  string 
around  the  two  pins  at  i  and  A  ;  having  fastened  the  loop, 
remove  the  pin  at  A  and .  substitute  a  pencil.  The  loop 
will  now  lie  around  the  two  pins  1-2,  and  a  regular  and  con- 
tinuous curve  will  be  produced  by  keeping  the  string  tant 
and  moving  the  pencil  around  from  point  A,  as  shown 
(the  original  of  this  drawing  was  actually  produced  by 
the  method  described).  In  practice,  with  large  curves,  a 
difficulty  is  experienced  in  preventing  the  string  stretching, 
and  so  interrupting  the  continuity  of  the  curve,  hence 
trammelling  is  more  often  resorted  to  in  the  workshop.  For 
draughtsmen's  work  a  silk  thread  is  often  employed. 

The  False  or  Three-Centred  "  Ellipse,"  Fig.  9.— This 
figure  is  drawn  with  compasses,  and  is  therefore  not  a  true 
elliptic  figure,  but  is  an  approximation  thereto,  much  used 


CONES  155 

by  bricklayers  for  setting  out   templets  for  what   they 
describe  as  "  elliptic  "  arches. 

Draw  the  span  or  major  axis  A  -A .  Divide  this  into  three 
equal  parts,  in  points  1-2.  With  these  points  as  centres, 
and  2- A  as  radius,  describe  circles  intersecting  in  point  3. 
Draw  lines  from  the  intersection  through  points  i  and  2 
to  cut  the  circles,  and  these  give  the  radius  for  describing 
the  central  part  of  the  curve,  the  two  ends  being  formed  by 
segments  of  the  circles  already  drawn.  It  will  be  seen  that 
only  two  shapes  are  required  for  the  bricks  in  this  arch. 

THE   CONE   AND   ITS    PROPERTIES 

Definitions- — There  are  two  kinds  of  cones — right  and 
oblique.  A  right  cone  has  its  axis  perpendicular  to  its  base  ; 
an  oblique  cone  has  its  axis  at  some  other  angle  than  a  right 
angle  with  its  base  (see  sketches,  Figs,  i  and  3,  page  156). 
The  axis  of  a  solid  is  a  straight  line  drawn,  or  imagined, 
connecting  the  centres  of  its  opposite  ends. 

A  right  cone  may  be  denned  as  a  solid  with  a  circular 
base,  and  sides  tapering  to  a  point.  It  may  also  be  de- 
scribed as  a  circular  pyramid.  When  the  top  portion  of  a 
cone  (or  other  similar  solid)  is  cut  off  parallel  with  its  base, 
the  remaining  portion  is  called  the  Frustum  (see  Fig.  2). 
When  the  line  of  section  is  oblique,  as  in  Fig.  4,  the  portion 
remaining  is  called  Ungula,  a  Latin  word  signifying  a  hoof, 
which  the  solid  somewhat  resembles. 

Projections  of  Cones,  Figs.  5  to  8,  are  respectively 
elevations  (or  sections,  as  they  are  exactly  alike)  and 
plans  of  a  right  cone  and  its  frustum ;  the  projectors  indi- 
cate how  the  plan  is  obtained  from  the  elevation.  Figs. 
9  and  10  are  the  projections  of  an  oblique  cone,  and  as  the 
method  of  obtaining  the  plan  is  similar  to  that  for  obtaining 
the  section  in  the  next  case,  its  explanation  will  be  dealt 
with  there. 

The  Conic  Sections  are  five  in  number,  named  re- 
spectively the^triangle,  see  Fig.  5,  a  section  through  the 


Fig.  I.  Ftg.2.  Fig.3. 


The  Conic  Sections  and  Coverings  of  Cones 


ELLIPTIC    SECTION    OF    CONE  157 

axis  and  diameter  of  its  base ;  the  circle  (see  Fig.  6) ,  a 
section  at  right  angles  to  the  axis  ;  the  ellipse  (see  Fig.  n«), 
a  section  through  the  two  inclined  sides  at  an  oblique 
angle  to  the  axis ;  the  parabola  (see  Fig.  14) ,  a  section 
through  one  side  and  the  base,  parallel  with  the  other  side ; 
and  the  hyperbola,  Fig.  16,  a  section  made  by  a  plane  pass- 
ing through  the  base  and  side  of  the  cone,  and  making  a 
greater  angle  with  the  base  than  the  side  of  the  cone  makes. 

It  is  not  possible  to  cut  a  cone  in  any  other  direction  than 
the  above  named,  and,  though  the  sizes  of  the  sections 
will  vary  according  to  their  positions  on  the  cone,  their 
shapes  will  be  constant.  It  may  be  noted  that  all  the  five 
figures  can  be  obtained  by  other  methods  than  as  sections 
of  cones,  but  no  other  solid  contains  them  all,  hence  the 
generic  term  of  conic  sections.  Some  geometricians  hold  that 
there  are  only  three  conic  sections,  because  the  triangle  and 
circle  are  common  to  other  solids,  and  they  define  these  as 
particular  cases  of  the  parabola  and  the  ellipse  respectively. 

The  Ellipse,  Fig.  n. — To  obtain  this  section,  draw  the 
elevation  of  the  cone  (and  it  may  be  here  interpolated  that 
it  will  be  advisable  for  the  student  to  draw  these  figures  at 
least  four  times  the  size  shown,  and  to  take  more  points 
than  are  shown  on  the  drawing,  where  they  are  limited  to 
avoid  a  confusion  of  lines)  and  the  line  of  section  as  A-B  ; 
project  the  extremities  to  the  base  b~b,  and  describe  a  semi- 
circle cutting  the  points  as  shown.  Divide  the  semicircle 
into  any  number  of  equal  parts  as  I,  2,  3,  4,  5,  6,  and  project 
these  upwards  to  cut  the  line  of  section,  then  project  ordin- 
ates  from  these  points,  at  right  angles  to  the  section  lines. 
Draw  a  line  a-b  across  them,  parallel  with  the  line  of  section 
(this  is  merely  done  for  convenience,  the  section  could  be 
drawn  upon  the  line  of  section  if  desired).  Make  each  of 
these  ordinates  equal  in  length,  on  each  side  of  the  line  a-b, 
to  the  corresponding  ordinate  in  the  semicircle,  which  is  a 
plan  of  the  section,  and  draw  the  outline  of  the  section 
through  the  points  so  found.  The  more  points  used  the 
truer  will  be  the  figure.  It  will  be  noticed  that  the  semi- 


158  PARABOLIC    SECTION    OF    CONE 

circle  might  equally  well  represent  the  half  plan  of  a  cylinder 
whose  sides  are  cut  by  the  line  A-B,  and  obviously  the  same 
section  would  be  obtained. 

The  Parabola,  Fig.  14. — To  produce  this,  draw  the  desired 
line  of  section  A-B,  Fig.  12,  and  divide  it  into  a  number  of 
equal  parts,  as  i,  2,  3,  4.  Through  these  points  draw  lines 
parallel  with  the  base,  and  cutting  the  sides  of  the  cone  in 
points  i',  2',  3',  4'.  These  lines  may  be  taken  to  represent  a 
series  of  horizontal  sections  of  the  cone,  and  their  planes  will 
becircles.  To  determine  their  size,  drop  projectors — dotted 
— into  the  plan,  cutting  the  diameter  in  a,  b,  c,  d ;  from  the 
middle  of  the  diameter  as  centre  and  these  points  as  radii, 
describe  concentric  circles.  Next  drop  projectors — full 
lines — from  points  i,  2,  3,  4,  and  the  extremities  in  the  line 
of  section  A-B,  into  the  plan,  cutting  the  appropriate 
circles  in  points  B",  i",  2",  3",  4",  a',  and  draw  a  curved  line 
through  these  points  on  each  side  of  the  diameter  as  shown  ; 
draw  also  the  plan  of  the  base  of  plane  of  section  B'-B",  thus 
obtaining  the  shape  of  the  section  in  plan.  To  obtain  its 
real  shape,  draw  the  line  a-d  parallel  with  A~B,  and  pro- 
ject ordinates  across  it,  from  the  points  in  section  line. 
Make  these  equal  in  length  on  each  side  of  a~d,  to  the  similar 
numbered  ordinates  in  the  plan,  measured  from  the  dia- 
meter b'-b",  and  draw  the  curve  through  the  points  so 
found. 

The  Hyperbola  (see  Fig.  16). — Two  plans  and  eleva- 
tions are  given,  the  first  pair  to  show  the  position  of  the 
line  of  section  E-D  in  elevation,  and  e~e'  in  plan.  Obviously 
we  are  looking  at  the  edge  of  the  section,  therefore  cannot 
see  its  shape.  To  obtain  this  the  plan  must  be  revolved  on 
its  centre  until  the  line  of  section  is  parallel  to  the  vertical 
plane.  This  is  shown  in  the  right-hand  plan,  and  a  new 
elevation  is  projected  from  it.  Divide  the  diameter  into 
a  number  of  equal  parts,  and  from  the  centre  describe 
circles  through  them  as  at  a",  b",  c",  e" ;  project  these  points 
into  the  elevation,  cutting  the  side  of  the  cone  in  a' ,  br,  c' ,  ef , 
and  draw  lines  through  them  parallel  to  the  base  :  these  lines 


COVERINGS    OF    CONES  159 

are,  of  course,  the  edges  of  sections  of  the  cone,  of  which 
the  circles  in  Fig.  15  are  the  respective  plans.  Next,  from 
points  a,  b,  c,  h,  where  the  circles  are  cut  by  the  line 
of  section,  raise  perpendiculars  to  intersect  the  horizontals 
in  elevation,  and  draw  the  curve  through  these  intersec- 
tions as  shown. 

To  obtain  the  Covering  of  a  Cone.— Let  Fig.  17  repre- 
sent the  plan  and  the  elevation  of  a  right  cone.  If  we 
divide  one-half  the  circumference  of  base  into  a  number  of 
equal  parts,  as  points  I  to  9,  and  project  these  to  the  base 
line  in  elevation,  then  draw  straight  lines  from  the  points 
to  the  apex  of  the  cone  a,  we  shall  have  the  elevations  of  a 
series  of  lines  drawn  at  equal  distances  apart  upon  the  sur- 
face of  the  cone,  and  by  their  aid  we  can  locate  a  point  or 
number  of  points  on  that  surface. 

To  obtain  the  Development  of  the  Semi-Cone 
(fl-i'-g). — With  point  a  as  centre  and  a-i'  (the  length  of 
side)  as  radius,  describe  an  arc.  Upon  this  set  out  an 
equal  number  of  spaces  as  shown  in  the  plan  ;  and  from 
the  last,  point  9',  draw  a  line  to  a. 

Then  the  space  bounded  by  the  lines  a-i',  g'-a  will 
exactly  cover  half  the  cone,  and  if  the  other  half  is  com- 
pleted similarly,  the  whole  surface  will  be  obtained. 

To  obtain  the  Development  of  Frustum  of  a  Cone 
as  shown  by  the  elevation,  C-D,  I'-Q,  proceed  as  described 
to  obtain  the  covering  of  the  entire  cone,  and  from  the  apex 
a  describe  an  arc  from  D,  the  top  of  the  frustum.  The 
portion  enclosed  between  the  two  arcs,  and  the  sides  D—i 
and  C'-Q',  is  the  covering  of  one-half  of  the  frustum. 

If  the  whole  cone  is  not  given,  all  that  is  necessary  to 
locate  point  a  is  to  produce  the  sides  of  the  frustum  until 
they  meet.  In  a  subsequent  example  (page  189)  a  further 
use  for  the  radial  lines  is  shown. 

The  Coverings  of  Domes. — A  dome  is  a  vaulted  roof 
having  a  circular,  elliptic  or  polygonal  plan.  The  first 
kind  are  termed  spherical  domes  or  vaults ;  the  second, 
ellipsoidal  domes  ;  the  third  are  specified  by  terms  indicating 


160  COVERINGS    OF    DOMES 

the  number  of  sides  to  the  plan,  as  square,  pentagonal, 
hexagonal,  octagonal,  etc.,  domes.  There  are  also  sub- 
varieties  due  to  differences  in  the  elevation  or  vertical 
sections,  such  as  ogee  domes,  gothic  or  pointed  domes, 
segmental,  etc. 

The  construction  of  the  dome,  depending  so  greatly  upon 
its  size  and  circumstances  of  location,  can  only  be  referred 
to  incidentally,  the  subject  of  this  section  being  the  method 
of  obtaining  the  true  shapes  of  the  coverings,  which  is 
common  to  all. 

A  dome  may  be  covered  either  by  boards  or  metal  sheets 
in  vertical  strips  called  "  gores,"  or  horizontal  bands  called 
"  zones/'  Both  methods  are  shown  in  the  case  of  the 
spherical  dome,  Figs.  I  and  2,  page  161.  We  will 
consider  the  vertical  method  first. 

Fig.  i,  B  and  C,  show  respectively  quarter  plans  of  the 
outside  and  inside  of  the  dome,  Fig.  2  being  the  interior 
and  exterior  elevations.  The  radial  lines  in  quadrant  B 
are  the  plans  of  the  joints  of  the  boards,  and  the  elliptic 
lines  in  Fig.  2  their  elevation.  Neither  set  of  lines  gives 
either  the  true  length  or  the  shape  of  the  edge,  but  both 
are  necessary  to  obtain  the  true  shape. 

To  obtain  the  Projection  of  the  Boarding.— Divide 
the  circumference  of  the  plan  into  as  many  segments  as 
the  width  of  the  boards  to  be  used  permits.  Draw  lines 
from  these  divisions  to  the  centre.  Next  divide  the  circum- 
ference in  the  elevation,  Fig.  2,  into  a  number  of  equal  parts 
as  i,  2,  3,  4.  Draw  indefinite  horizontal  projectors  from 
these  points,  also  vertical  projectors  into  the  plan,  cutting 
the  diameter  in  points  i,  2,  3,  4.  With  these  points  as 
radii,  describe  arcs  from  the  centre  of  the  plan,  and  pro- 
jectors taken  up  from  their  intersections,  with  the  various 
joint  lines,  to  the  corresponding  horizontals,  will  give  points 
in  the  elliptic  curves  forming  the  edges  of  the  boards. 
Only  one  set  of  these  projectors  has  been  taken  up,  sufficient, 
however,  to  indicate  the  method  ;  these  are  distinguished 
by  chain  lines,  the  points  found  are  marked  I.,  II.,  III.,  IV. 


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162  SPHERICAL    DOMES 

Taking  the  joint  at  N,  the  projectors  are  shown  starting 
from  points  i',  2',  3',  4',  and  locate  points  n,  I,  II,  III,  IV 
on  the  horizontals  in  Fig.  2.  Draw  the  curve  through 
these  points.  We  have  next  to  discover  the  true  shape  of 
the  board.  Bisect  the  width  of  any  board  in  plan  and 
draw  a  line  from  the  centre  through  the  point,  extending 
it  indefinitely  as  shown.  Mark  off  upon  this  line  points 
i",  2",  3a,  4a,  5a>  equal  in  length  to  the  like  numbered 
points  upon  the  circumference  in  elevation — that  is,  make 
a  stretch-out  of  the  curved  line.  Draw  perpendiculars  to 
the  mid  line  through  these  points  and  make  them  equal  in 
width  to  the  corresponding  portions  of  the  respective  arcs, 
passing  across  the  plan  of  the  same  board — -i.e.  ia  is  made 
equal  to  the  stretch  out  of  arc  i  in  the  plan,  and  so  on. 
In  the  scale  drawing  it  is  near  enough  to  make  each  ordi- 
nate  equal  to  a  straight  line  across  the  plan,  but  when 
setting  out  full  size  it  is  necessary  either  to  develop  the 
segment  of  the  arc  or  to  make  due  allowance  in  the  width 
for  the  curving  of  the  board  when  nailed  down  to  the  purlins. 
Having  thus  obtained  a  series  of  points  on  the  ordinates, 
draw  the  curved  edges  through  them.  One  mould  will 
answer  for  all  the  boards. 

To  obtain  Shape  of  Boards  laid  horizontally  as 
shown  at  A,  Fig.  i,  which  may  be  taken  to  represent  a  half 
elevation  of  a  dome  covered  in  six  zones. — As  the  boards 
have  to  be  marked  and  cut  whilst  flat,  it  is  necessary  to 
convert  the  spherical  surface  into  a  series  of  planes,  by 
drawing  chords  of  straight  lines  between  the  ends  of  the 
segments  of  the  circumference  intersected  by  the  joints. 

If  we  extend  these  chords  until  they  intersect  a  perpendi- 
cular or  "  pole  "  from  the  centre  of  the  dome,  we  can  deal 
with  the  projection  of  each  board  as  if  it  were  the  section 
of  a  cone,  and  as  the  development  of  the  surface  of  a  cone 
has  been  fully  explained  on  page  159,  it  will  only  be  neces- 
sary to  recapitulate  here. 

Take  No.  2  board  as  example.  Produce  its  chord  line  to 
meet  the  centre  line  in  point  II.  This  becomes  the  apex 


GOTHIC    DOMES  163 

of  its  cone.  From  this  point  as  centre,  and  the  upper  and 
lower  edges  of  the  board  as  radii,  describe  arcs  indefinitely. 
Next  project  the  ends  of  the  chord  to  the  base  as  at  a-b ; 
these  projectors  are  shown  in  chain  line.  From  the  centre, 
with  the  points  a-b  as  radii,  describe  arcs,  which  will 
represent  the  lower  edges  of  the  boards,  Nos.  2  and  3,  in 
plan.  Note,  to  avoid  confusion  with  the  previous  board- 
ing, these  plan  lines  are  drawn  in  the  quarter  plan  D,  and 
numbered  2  and  3  respectively.  These  lines  represent  also 
the  base  and  frustum  of  the  cone  we  are  to  develop,  and  we 
divide  the  quadrant  into  a  number  of  equal  parts,  stepping 
off  the  same  number  on  the  lower  edge  of  the  development 
of  board  No.  2.  Join  the  last  point,  No.  7,  to  the  apex  and 
the  length  and  shape  of  the  board  is  determined.  Of  course 
the  actual  length  of  the  board  will  depend  upon  the  situation 
of  the  ribs,  also  the  width  of  stuff  available  from  which  the 
curved  segment  is  to  be  cut.  The  other  boards  are  found 
in  a  similar  manner,  each  board  having  its  special  "  cone." 
The  respective  apices  are  numbered  ///,  IV,  V.  The 
lowest  board,  No.  I,  has  its  apex  beyond  the  edge  of  the 
page,  and  would  be  set  out  in  full  size  by  the  three-point 
method  of  drawing  an  arc.  It  will  be  noticed  that  with 
the  vertical  method  of  boarding  it  is  necessary  to  use  purlins, 
and  these  are  made  to  lie  perpendicular  to  the  curve.  Two 
of  these  purlins  are  shown  in  the  quarter  plan  C.  When 
horizontal  method  of  boarding  is  adopted,  the  ribs  must  be 
placed  much  closer  together,  consequently  thinner  stuff 
may  be  used  than  with  the  vertical  method.  The  dome 
shown  is  supposed  to  be  about  8  feet  in  diameter.  As 
the  interiors  of  these  small  domes  are  not  seen,  it  is  usual 
to  leave  the  inner  edges  of  the  ribs  straight ;  the  purlins 
are  shaped  to  reduce  the  weight. 

A  Gothic  or  Pointed  Dome  is  shown  in  Figs.  3  and  4. 
These  are  usually  boarded  vertically,  and  the  ribs  are  all  of 
the  same  shape,  the  radius  of  the  arc  being  equal  to  the 
span.  The  purlins  are  in  such  case  placed  horizontally, 
and  are  of  just  sufficient  thickness  to  take  the  nails  without 


1 64  ELLIPTIC    DOMES 

splitting,  their  width  affording  all  the  strength  required. 
They  need  not  equal  the  ribs  in  depth,  and  the  housing  to 
receive  their  ends  should  be  stopped,  as  shown  in  the 
elevation  of  second  rib,  to  afford  an  abutment. 

The  plan,  Fig.  3,  shows  at  A ,  plan  of  the  boarding,  at  B 
plan  of  purlins  and  curb,  at  C  the  geometrical  construction 
for  projection  of  ribs  and  shape  of  the  boarding. 

To  project  the  Ribs  in  Elevation.— Having  first  de- 
scribed the  outline  of  roof,  by  arcs  struck  from  points  C  and 
C,  divide  the  curve  of  one  side  into  a  number  of  parts,  and 
drop  projectors  into  the  plan,  cutting  the  diameter  in  points 
!>  2>  3>  4>  5'  6.  Carry  round  these  points  to  the  face  of  the 
rib  to  be  projected,  by  circles  struck  from  the  centre. 
These  new  points  are  marked  i°,  2°,  3°,  4°,  5°.  Project  them 
upwards  to  cut  horizontals  drawn  from  the  original  points 
in  the  elevation,  and  draw  the  curve  through  the  inter- 
sections. The  development  of  the  boards  is  obtained  as 
explained  for  a  spherical  dome. 

An  Elliptic  Dome  is  shown  in  Figs.  5  and  6.  The  solid 
on  which  this  is  based  is  termed  an  ellipsoid,  the  geo- 
metrical definition  of  which  is  a  solid  produced  by  the 
revolution  of  ah  ellipse  upon  its  axis.  Obviously,  any 
section  of  the  solid  passing  through  the  generating  axis  will 
be  an  ellipse,  and,  as  when  anything  revolves,  its  path  must 
be  a  circle,  any  section  perpendicular  to  the  axis — -i.e. 
parallel  with  the  transverse  axis — will  be  a  circle.  We  know 
from  this  that  in  an  elliptic  dome  with  its  ribs  arranged 
as  shown  in  the  plan,  Fig.  5,  all  the  ribs  will  be  of  the  same 
contour,  and  that  the  covering  boards  must  also  be  all  alike. 
The  procedure  to  obtain  the  projections  and  development 
of  the  covering  is  precisely  as  in  the  last  case. 

THE    DRAWING   OF   ARCHES — BRICK  AND    STONE    (page    165) 

The  Gauged  or  Flat  Arch,  Fig.  i,  is  employed  only 
in  comparatively  narrow  openings,  and,  though  generally 
drawn  straight  upon  the  soffit  or  underside,  is  really  slightly 


165  GAUGED    ARCHES 

cambered  or  curved  upwards  in  practice,  when  made  in 
brickwork.  The  term  "  gauged  "  is  applied  to  these  because 
the  bricks  are  cut  to  a  gauge  or  templet,  to  ensure  them  being 
the  right  size  and  shape  in  each  course.  The  method  of 
setting-out  to  be  described  is  that  pursued  to  obtain  the 
templets.  Draw  a  centre  line  and  set  off  the  width  of 
opening  on  each  side.  Draw  the  soffit  line  perpendicular 
to  the  centre  line,  and  measure  upwards  as  many  courses 
as  the  arch  is  to  be  deep,  which  in  the  example  is  four.  The 
exact  height  will  vary  with  the  character  of  the  work  and 
must  be  measured  directly  therefrom.  Having  found  this, 
draw  the  back  or  extrados  line  horizontal — -that  is,  parallel 
with  the  soffit  line  already  drawn.  Set  up  on  the  centre 
line,  the  camber,  which  should  be  J  in.  for  each  foot  of 
span,  and  either  bend  a  lath  around  to  the  three  points 
and  mark  the  curve  by  its  aid,  or  use  the  turning-piece  for 
the  purpose.  Next  determine  the  angle  of  skewback  which 
locates  the  common  centre  of  the  arch.  There  are  various 
methods  and  ratios  adopted  for  this.  A  common  one  is  to 
make  J  in.  the  depth  of  arch,  the  amount  that  the  back  is 
longer  than  the  soffit  on  each  side  ;  another,  to  add  ij  in.  for 
each  foot  in  span.  This  latter  met  hod  is  shown  in  the  example. 
Produce  the  line  of  skewback  to  meet  the  centre  line,  and 
all  the  joints  are  drawn  to  the  intersection.  From  this 
centre,  with  radius  equal  the  height  to  the  crown,  describe 
an  arc,  and  upon  this  set  out  the  voussoirs  equally,  starting 
with  the  key,  which  should  be  spaced  equally  on  each  side 
the  centre  line ;  draw  the  bed  joints  horizontal,  and  all  the 
lines  are  then  obtained  for  marking  the  templets.  The 
hidden  discharging  arch  at  the  back,  which  carries  the  load, 
is,  of  course,  not  set  out  on  the  rod,  the  necessary  "  pitch  " 
being  given  to  bricks  in  the  jointing,  when  laying  them  over 
the  core  or  bed,  but  in  making  the  drawing  on  paper,  start 
the  skewback  just  clear  of  the  end  of  the  wood  lintel,  which 
is  usually  tailed  into  the  wall  the  depth  of  half  a  brick,  and 
pitch  it  60°  to  find  the  centre  for  striking  the  curves. 
The  Mason's  Flat  or  Camber  Arch,  Fig.  3,  shows 


OBTAINING    TEMPLETS  167 

two  methods  of  jointing :  stepped  joints  on  the  left  and 
joggle  joints  on  the  right.  All  the  joints  radiate  from  a 
common  centre,  which  is  not  the  centre  of  the  camber,  but 
is  placed  according  to  taste.  The  "  skewback  "  is  horizontal, 
as  there  is  no  spreading  thrust  on  this  arch. 

The  Round,  Roman  or  Semicircular  Arch,  as  it  is 
variously  termed,  Fig.  4,  shows  two  methods  of  treatment 
in  stone  arches.  The  stepped  or  rebated  voussoirs  on  the 
right,  with  curved  extrados,  are  used  when  all  the  structure 
is  in  stone  and  appearance  is  of  less  importance  than  strength. 
The  step  extrados  arch  shown  on  the  left  is  chiefly  used  in 
conjunction  with  brickwork,  the  back  joints  of  the  arch 
falling  on  the  course  joints  of  the  brickwork,  the  perpend 
being  a  multiple  of  3  in. 

The  Elliptic  Arch,  Fig.  5,  is  shown  in  stone  on  the  left 
side  and  bricks  on  the  right.  In  the  first,  which  is  a  true 
ellipse  drawn  as  described  on  page  153,  the  voussoirs  are 
worked  out  to  a  level  seating  with  bed  joints  normal  or 
perpendicular  to  the  curve,  at  the  points  they  occur.  The 
setting  out  is  shown,  and  is  described  on  page  154.  The 
right  half  shows  the  four  centred  or  "  bricklayers'  ellipse," 
which,  being  composed  of  segments  of  circles,  is  not  an 
ellipse  at  all,  as  no  part  of  a  true  elliptic  curve  can  be  struck 
with  compasses  ;  but  it  is  a  convenient  arrangement,  as  only 
two  templets  are  required  for  the  voussoirs,  whilst  in  a  true 
ellipse  a  separate  templet  is  required  for  each  voussoir.  To 
draw  this  arch,  construct  a  rectangle  on  the  springing  line 
and  rise  ;  divide  the  half  span  and  the  rise  each  into  three 
equal  parts,  as  at  I,  2,  4,  5.  Set  off  on  the  centre  line  point 
h  at  a  distance  below  the  springing  equal  to  the  rise  above 
it.  Draw  a  line  from  h,  through  point  I,  until  it  intersects 
a  line  drawn  from  point  5  to  the  crown  in  point  b  ;  then  draw 
chord  lines  from  b  to  the  spring  and  crown  ;  bisect  these 
two  lines  and  produce  the  bisectors  until  they  cut  the  centre 
line  and  the  line  h-b  in  points  c  and  cr.  These  points  are  the 
centres  of  the  curves  and  the  bed  joints  of  the  voussoirs  are 
drawn  to  them. 


168  GOTHIC    ARCHES 

The  False  Ellipse,  Fig.  6,  is  another  method  of  de- 
scribing an  approximation  to  an  ellipse  which  has  been 
fully  described  on  page  155. 

Pointed  arches  are  typical  of  the  so-called  Gothic  styles 
of  architecture,  and  they  are  always  formed  by  combina- 
tions of  segments  of  circles.  The  simplest  and  earliest 
form  is  the 

Lancet  Arch,  Fig.  7.  This  is  always  described 
with  radii  greater  than  the  span,  but  varying  according 
to  requirements.  In  the  example  they  equal  one  and  a  half 
times  the  span.  The  bed  joints  are  drawn  to  the  centre 
from  which  the  segment  is  struck. 

The  Equilateral  Arch,  Fig.  8,  has  its  radii  equal  to  the 
span,  the  centres  being  at  the  opposite  springings.  The 
bed  joints  are  sometimes  made  to  radiate  from  the  centres, 
but  a  better  appearance  is  obtained  by  dividing  up  the  soffit 
and  springing  equally  in  the  following  manner.  Ascertain 
how  many  voussoirs  are  required  on  either  side  ;  then  divide 
the  springing  line  between  the  centre  of  the  opening  and 
the  extremity  of  the  extrados  into  as  many  equal  parts  as 
there  are  to  be  voussoirs,  not  counting  the  keystone.  In 
the  example,  six  are  taken  for  the  stone  arch  and  fifteen  for 
the  brick  arch.  Divide  the  soffit  between  springing  and 
keystone  into  the  same  number  of  parts  and  join  the  points 
as  shown,  producing  the  lines  across  the  face  of  the  arch  to 
obtain  the  bed  joints. 

The  Tudor  or  Four-Centred  Arch,  Fig.  9,  typical  of 
the  latest  period  of  Gothic  architecture,  is  constructed  from 
four  centres,  two  in  the  springing  and  two  in  the  reveals 
below.  To  draw,  divide  the  span  on  the  springing  line  into 
four  equal  parts  ;  on  that  portion  of  the  springing  lying 
between  the  two  outer  divisions  construct  an  equilateral 
triangle  as  shown,  and  produce  the  sides  to  intersect  the 
jambs  or  reveals.  A  horizontal  line  joining  the  intersections 
will  form  the  base  of  a  second  equilateral  triangle,  and  the 
two  base  angles  in  each  case,  points  i,  2,  3,  4,  contain  the 
centres  for  describing  the  arcs.  The  sides  of  the  triangles 


SQUINCH    ARCH  169 

produced  across  the  face  of  the  arch  give  the  leading  bed 
joint,  and  the  point  of  junction  of  the  respective  arcs.  The 
bed  joints  in  each  section  are  made  to  radiate  from  the 
centre  from  which  that  section  is  described. 

The  Horseshoe  or  Moorish  Arch,  Fig.  16,  is  generally 
associated  with  Saracenic  or  Arabic  architecture  ;  elsewhere 
it  is  used  as  an  ornamental  rather  than  a  constructional 
feature.  Alternative  treatments  are  shown,  the  principal 
characteristic  being  the  carrying  of  the  curve  around  below 
the  centre  line,  no  other  type  of  arch  sharing  this  peculiarity. 

The  Stilted  Arch,  Fig.  i2a,  which  springs,  not  from 
the  impost  where  all  other  arches  commence  but  at  some 
distance  above,  was  a  constructional  device  in  Early  English 
architecture  to  bring  the  crowns  of  cross  vaulting  into  line 
or  level.  Apart  from  this  peculiarity,  there  is  no  distinctive 
feature  from  the  ordinary  arch,  and  "  stilting  "  may  be 
applied  to  arches  of  any  contour. 

The  Basket-handle  or  Three-centred  Arch,  Fig.  13, 
is  obtained  by  dividing  the  span  into  three  equal  parts  and 
constructing  an  equilateral  triangle  upon  the  centre  part,  as 
shown.  The  three  angles  of  the  triangle  contain  the  centres, 
and  the  sides  produced  across  the  face  of  the  arch  give  the 
leading  bed  joint  and  junction  of  the  curves. 

The  Ogee  Arch,  Fig.  14,  is  described  in  detail  under 
Carpentry  Arches. 

The  Squinch  Arch,  Fig.  15,  is  so  named  from  its  position, 
not  its  shape,  which  may  vary  with  circumstances.  Squinch 
is  Old  English,  or  Saxon,  for  corner,  and  in  this  connection 
means  an  arch  turned  across  a  corner.  It  is  often  used  to 
support  a  diagonal  wall  beneath  an  octagonal  spire,  where 
the  tower  changes  from  square  to  octagonal. 

The  other  sketches,  Figs.  10,  n,  12,  are  comparative 
groupings  of  four  chief  types  of  arches:  the  "flat,"  the 
"  segmental,"  the  "  round  "  and  the  "  pointed." 

Carpentry  Arches,  page  171. — The  arched  frames 
constructed  by  the  carpenter,  or,  to  be  exact,  the  joiner, 
usually  follow  the  contour  of  the  openings  provided  by  the 


i/o  CARPENTRY    ARCHES 

mason  or  bricklayer,  consequently  their  description  or 
setting  out,  so  far  as  the  outlines  are  concerned,  is  similar 
to  that  described  for  stone  arches.  There  are,  however, 
di  (Terences  in  detail,  and  the  necessity  of  dealing  with  these 
gives  the  opportunity  of  presenting  alternative  treatment  of 
types  that  will  be  equally  useful  to  the  mason  and  the 
carpenter. 

The  Equilateral  Arched  Frame,  Fig.  i,  is  described 
upon  an  equilateral  triangle,  the  radius  of  the  two  arcs  being 
equal  to  the  span  ;  the  centres,  therefore,  lie  in  the  springing 
line  at  a  and  b.  The  back  of  the  frame  is  described  from 
the  same  centres.  The  haunch  joints  are  usually  placed 
about  one-quarter  the  height  of  the  arch  above  the  springing, 
and  radiate  from  the  centre  of  the  curve — i.e.  they  are  made 
normal  to  the  direction  of  pressure. 

The  Lancet,  Fig.  2,  is  described  by  constructing  two 
semicircles  on  the  springing  line  extended,  with  a  radius 
equal  to  half  the  span,  the  centres  being  at  a  and  b.  The 
extremities  of  these  semicircles,  points  I  and  2,  provide  the 
centres  for  striking  the  curves.  The  haunch  joint  is  one- 
fourth  the  perpendicular  height  above  the  springing. 

The  Drop  Arch,  Fig.  3,  is  made  in  varying  degrees  of 
depression  to  suit  the  designer.  The  span  and  rise  being 
given,  construct  a  triangle  upon  the  springing  line  with  the 
required  altitude.  Bisect  the  inclined  sides  of  the  triangle 
and  produce  the  bisectors  to  intersect  the  springing  line 
in  points  I  and  2.  These  are  the  required  centres. 

The  Tudor  Arch,  Fig.  4,  is  constructed  by  dividing  the 
span  on  the  springing  line  into  four  equal  parts,  describing 
semicircles  equal  in  radius  to  the  half  span,  upon  points 
I  and  3  as  centres  ;  these  describe  the  haunch  arcs.  For 
the  centres  of  the  crown  arcs,  describe  quadrants  from  a  and 
b,  intersecting  the  jambs  in  points  2  and  4,  which  are  the 
required  centres.  To  find  the  joint  line,  join  points  1-2 
and  produce. 

Two  other  Four-centred  Arches  are  shown  in  Fig.  5. 
On  the  right  half  the  span  is  divided  into  six  equal  parts, 


i;2  COMPOUND    CURVES 

and  a  perpendicular  dropped  from  I  and  5.  These  points 
are  also  the  centres  of  the  quadrants  containing  the  lower 
centres,  and  the  remainder  of  the  construction  is  clearly 
indicated  in  the  figure.  On  the  left  the  span  is  divided 
into  four  equal  parts,  and  an  equilateral  triangle  constructed 
upon  the  middle  two  give  the  centres  as  shown. 

The  Cyma  Reversa  or  Wave  Arch,  Fig.  6,  is  produced 
upon  a  triangle  of  60°,  the  span  a~b  forming  the  base.  Bisect 
the  inclined  sides  a-c  and  b-c  in  points  e  and  g,  and  draw  a 
line  through  the  points  parallel  with  a~b.  With  e  and  g  as 
centres  and  the  length  e-g  as  radius,  describe  the  arcs  e-c 
and  g-c.  With  the  same  radius,  describe  arcs  from  a  and  b, 
intersecting  the  line  of  centres  in  d  and  /.  These  locate 
the  two  centres  for  the  remaining  arcs  of  the  curve. 

The  Ogee  Arch,  Fig.  7,  is  a  form  frequently  adopted  for 
pavilion  roofs,  also  for  window  frames.  To  describe  it, 
construct  an  equilateral  triangle  on  the  span.  From  the 
three  angles  of  the  triangle  with  radius  equal  half  the  span, 
describe  arcs  intersecting  the  sides  as  shown  at  the  points 
of  intersection  ;  describe  other  arcs  intersecting  the  first, 
in  points  i,  2,  3.  These  points  furnish  the  centres  for 
describing  the  curves.  A  line  joining  points  1-2  or  1-3 
gives  the  position  and  direction  of  the  joints. 

The  Bell  Arch  or  Reversed  Ogee,  Fig.  8,  is  drawn 
similarly.  Join  the.  crown  to  the  springing  by  the  line  c-s. 
Bisect  this  line,  which  gives  the  point  of  junction  of  the 
curves  of  contrary  flexure.  With  a  radius  equal  to  half 
the  length  of  c~s,  describe  intersecting  arcs  above  and 
below  the  line.  These  intersections  give  the  centres  of  the 
required  arcs.  If  a  joint  is  required  it  must  be  upon  a  line 
joining  the  centres  of  the  reverse  arcs. 

Compound  Curves.— There  are  many  of  these,  and  a  few 
that  are  considered  of  most  service  to  artisans  in  the  building 
trades  are  dealt  with. 

The  Helix,  Figs,  i  and  2,  page  173,  are  the  plan 
and  elevation  respectively  of  a  cylindric  helix,  sometimes 
miscalled  a  spiral.  The  spiral  is  a  curve  of  continually 


1741.  THE    HELIX 

diminishing  radius,  no  two  portions  being  alike.  The 
helix  is  a  curve  of  constant  distance  from  its  axis  of  revolu- 
tions, its  opposite  portions  being  symmetrical.  The  plan  of 
a  helix  may  be  a  circle  or  an  ellipse  ;  the  elevation  is  similar 
in  each  case.  The  projection  of  a  helix  as  shown  in  Fig.  2 
does  not  give  its  true  contour,  because  the  curve  itself  is 
formed  upon  a  cylindric  surface,  whilst  the  projection  is 
upon  a  plane  ;  but  the  projections  are  necessary  for  many 
purposes,  one  of  which  is  shown  in  Figs.  4  and  5.  Fig.  3  is 
the  development  of  the  helical  curve  shown  in  Fig.  2,  b-c 
being  the  helix,  which,  it  will  be  observed,  is  a  straight  line. 
a-b  represents  the  distance  which  one  revolution  of  the  helix 
rises  or  advances,  and  this  is  called  the  "  pitch,"  a  term  which 
is  not  strictly  correct ;  the  distance  a-b  upon  either  figure 
gives  the  amount  of  pitch  or  inclination  of  the  curve,  but  it  is 
not  the  inclination  itself.  In  the  example,  one  in.  (by  scale) 
is  taken  for  each  complete  revolution  of  the  line  ;  therefore 
such  a  helix  is  termed  one  of  an  inch  pitch.  A  common 
example  is  the  thread  of  a  screw.  The  distance  between  the 
highest  part  of  a  thread  and  the  highest  part  of  the  next  one 
above  it,  upon  the  same  side,  gives  the  "  pitch  "  of  that 
screw,  otherwise  expressed,  as  so  many  threads  to  the  inch. 
To  draw  the  Helix. — Describe  a  circle  of  the  required 
diameter ;  divide  this  into  a  number  of  equal  parts,  as  shown 
in  Fig.  i.  Draw  a  line  parallel  with  one  diameter,  and  erect 
a  perpendicular,  as  a-B.  Set  off  upon  this  the  desired  rise 
or  amount  of  "  pitch  "  for  one  revolution,  as  a- A.  Divide 
this  space  into  the  same  number  of  equal  parts  as  the  plan, 
and  number  them  similarly.  Next  draw  projectors  from 
each  point  upon  the  circumference  of  the  circle  into  the 
elevation,  and  intersect  them  by  horizontal  projectors  drawn 
from  the  correspondingly  numbered  divisions  between  a- A . 
Trace  the  curve  through  the  points  so  found.  If  desired, 
intermediate  points  may  be  used  to  facilitate  the  freehand 
drawing,  as  shown  by  the  dotted  line  between  the  points  2-3 
and  its  projector,  shown  in  full  lines.  Note  that  at  each 
revolution  the  curve  repeats  upon  the  projection. 


A    WREATHED    HANDRAIL  175 

To  draw  the  Development,  Fig.  3.— Make  the  straight 
line  a-c  equal  in  length  to  the  circumference  of  the  helix  in 
plan  ;  draw  a-b  perpendicular  and  equal  in  length  to  the 
given  rise  a-A,  Fig.  2  ;  join  b-c,  then  b~c  is  the  true  inclina- 
tion of  the  helix.  A  wreathed  handrail  to  a  circular  stair 
is  an  example  of  a  helical  curve,  and  in  Fig.  5  a  projection 
of  one  is  given. 

To  drawthe  Projection  of  aWreathed  Handrail.— Let 
Fig.  4  be  the  plan  of  the  rail  and  the  radiating  lines  may  be 
considered  the  risers  of  the  steps  beneath.  For  convenience 
of  explanation  we  will  consider  first  the  outside  of  the  rail 
in  plan,  and  the  under  arris  in  elevation.  Draw  the  per- 
pendicular 1-8,  Fig.  5,  as  a  projection  of  point  I  in  the  plan ; 
set  off  upon  it  eight  divisions  equal  to  the  distance  between 
the  points  in  plan  ;  this,  of  course,  would  not  be  so  in  practice. 
The  "  rise  "  of  a  step  is  always  less  than  its  "  going,"  but  the 
above  arrangement  facilitates  explanations. 

Draw  horizontal  projectors  from  each  division  and  inter- 
sect them  by  perpendiculars  from  the  correspondingly 
numbered  points  in  the  plan.  Draw,  either  freehand  or  by 
aid  of  the  French  curve,  a  continuous  line  through  the  points 
so  found.  This  will  produce  the  lower  external  arris  as 
shown.  Now  if  we  consider  the  rail  to  have  vertical  sides, 
as  it  actually  does  in  practice,  before  it  is  moulded,  it  will  be 
obvious  that  the  top  external  arris  will  be  directly  over  the 
line  just  drawn,  and  is  represented  in  the  plan  by  the  same 
circle.  Therefore  all  that  is  necessary  to  obtain  the  pro- 
jection of  the  top  edge  is  to  utilise  the  same  projectors  by 
producing  them  upwards  as  shown  in  full  line,  and  making 
them  equal  in  length  to  the  thickness  of  rail ;  a  second 
series  of  points  will  thus  be  obtained  through  which  to  draw 
this  curve.  The  two  inner  arrises  are  obtained  similarly, 
but  in  this  case,  though  we  use  the  same  heights  as  before,  we 
project  from  the  inside  circle  in  plan,  as,  for  example,  on 
radiator  3,  point  III  taken  into  the  elevation  becomes 
point  ///'  upon  the  horizontal  projector  3.  As  the  rail 
winds  around  the  cylinder  the  view  of  the  inner  edge  is 


i/6  THE    RISING    SPIRAL 

intercepted  by  the  outside  of  the  rail,  therefore  that  portion 
is  shown  by  a  dotted  line. 

The  Spiral  is  a  curved  line  whose  consecutive  points 
continuously  and  uniformly  approach  or  recede  from  a 
certain  fixed  point  called  the  pole.  A  line  drawn  from  the 
pole  to  any  point  in  the  curve  is  called  its  radius  at  that 
point.  Herein  lies  the  essential  difference  between  a  true 
spiral  and  a  helix  ;  the  radii  of  a  helix  are  all  of  one  length  ; 
the  radii  of  a  spiral  are  all  of  different  lengths.  The  spiral 
ascends  upon  a  cone,  the  helix  upon  a  cylindric  or  ellipsoidial 
prism. 

To  draw  a  Spiral  Curve.— Draw  the  generating  cone 
and  its  plan  as  Figs.  6  and  7.  Divide  the  plan  into  any 
number  of  segments  by  radial  lines  through  its  centre. 
Project  their  extremities  into  the  elevation,  as  indicated  by 
the  figures.  Join  the  points  upon  the  base  to  the  apex,  thus 
producing  a  series  of  lines  upon  the  surface  of  the  cone  of 
which  the  first  drawn  radial  lines  are  the  plans.  Next 
erect  a  perpendicular  to  the  base,  and  upon  it  set  off  the 
same  number  of  equal  divisions  as  are  shown  in  the  plan. 
These  may  bear  any  proportion  to  the  "  going  "  in  the  plan, 
and,  as  in  the  helix,  they  indicate  the  pitch.  Draw  horizontal 
projectors  from  these  divisions  2,  3,  4,  etc.,  to  the  corres- 
pondingly numbered  sections  upon  the  surface  of  the  cone, 
and  trace  the  curve  through  the  points  so  found  ;  this  gives 
us  the  "  rising  spiral." 

To  find  the  plane  or  spiral  "  scroll/'  Fig.  6,  drop  per- 
pendiculars from  the  points  found  on  the  surface  of  the  cone 
upon  the  similarly  numbered  radii  in  the  plan,  as,  per  ex- 
ample, ////  to  4",  and  trace  the  curve  through  these  points. 

The  Scroll,  Fig.  9,  is  a  plane  spiral  curve,  also  known 
as  the  volute.  There  are  several  methods  of  drawing  these 
by  diminishing  arcs  of  circles ;  some  more  applicable  to 
handrails  are  given  in  the  author's  "  Modern  Practical 
Joinery."  The  one  described  here  is  more  suitable  for  archi- 
tectural draughtsmen. 
We  have  first  to  obtain  proportional  radii,  see  Fig.  9. 


SCROLLS  177 

Draw  a-b  equal  in  height  to  the  largest  radius  required  or 
given  ;  number  this  i.  At  right  angles,  draw  a~c  at  any 
convenient  length  ;  join  b-c.  We  have  next  to  decide  how 
many  centres  to  use  ;  this  is  a  matter  of  judgment  and  de- 
pends upon  the  size  of  the  scroll.  In  the  example,  ten  has 
been  chosen.  Then  divide  a-b  into  ten  equal  parts  ;  at  the 
eighth  part  draw  a  line  parallel  to  a~c,  intersecting  b-c  in  X ; 
draw  a  perpendicular  to  a-c  from  this  point,  which  gives 
No.  2  radius.  Next  join  point  8  to  c,  and  where  this  line 
intersects  radius  2,  draw  a  similar  horizontal  to  the  first,  and 
so  obtain  radius  3  ;  proceed  in  like  manner  to  the  tenth. 
We  have  now  a  series  of  radii  reduced  in  geometrical  pro- 
gression. To  use  them,  take  radius  No.  i  in  the  compasses 
and  describe  a  quadrant  as  in  Fig.  8.  Draw  lines  from  the 
centre  at  right  angles  to  each  other,  and  upon  the  one  at 
which  the  arc  finishes  set  off  the  second  radius,  marked 
centre  2,  measuring  from  the  circumference.  Describe  a 
quadrant  with  this,  and  proceed  in  like  manner  with  the 
remaining  radii.  The  scroll  might  be  continued  until  it 
finished  into  the  "  eye  "  or  point,  but  to  do  so  would  hide 
some  of  the  centres  and  make  the  drawing  less  clear. 

In  Fig.  8  the  numbers  are  placed  close  to  the  centres  from 
which  the  radii  spring,  and  they  read  towards  the  radii  they 
refer  to. 


CHAPTER   XI 
WORKSHOP   DRAWINGS 

Difference  between  "  Working  "  and  "  Workshop  "  Drawings. 
Methods  of  preparing  Workshop  Drawings  for  Various 
Trades.  JOINERS'  RODS  —  difference  between  setting-out 
material  and  setting-out  rods.  Purposes  of  a  Rod — what  it 
should  contain,  and  what  it  should  not.  Standard  Widths  of 
Rods.  How  to  indicate  Sections,  Broken  Sections,  Dimension 
Lines.  Method  of  dealing  with  Long  Rods.  Where  to  start 
Setting-out.  Datum  Points.  Setting-out  a  Venetian  Window — 
details  of  procedure.  A  Pair  of  Circular-headed  Doors  and 
Finishings — the  necessary  Rods.  What  the  "  Height  Rod  " 
should  contain.  The  Elevation  Rod — method  of  setting  it  out. 
The  Question  of  Joints.  BRICKLAYERS'  SETTING-OUT.  A  Semi- 
circular Arch  in  a  Circular  Wall,  with  Parallel  Jambs  and  Level 
Soffit — drawback  of  the  "centre  "  method.  The  Geometrical 
Method,  obtaining  Templets  and  Soffit  Mould.  A  Circle-on- 
Circle  Opening  with  splayed  Jambs  and  Soffit.  Producing  the 
Section.  Obtaining  Soffit  Mould.  Setting  out  an  Octagonal 
Chimney  Stack.  Alternative  Methods  of  Setting  out  Octagons. 
Obtaining  the  Bevels  for  cutting  Templets 

THE  term  "  workshop  drawing  "  is  used  to  differentiate 
those  drawings  prepared  directly  for  the  workman's  use  in 
setting  out  his  material ;  from  the  detail  drawings  prepared 
by  an  architect  for  the  use  of  the  builder,  which  are  generally 
known  as  working  drawings.  (For  a  fuller  definition  of  these, 
see  Chapter  I.)  In  a  sense,  both  of  these  kinds  of  drawings 
can  be  said  to  be  working  drawings,  as  they  have  to  be 
"  worked  "  to,  but  in  the  case  of  small  scale  drawings  a 
certain  amount  of  translation  or  calculation  is  necessary 
before  the  work  can  be  put  in  hand,  whilst  the  drawings  now 
to  be  described  are  invariably  made  full  size,  so  that  the 
workman  can  apply  his  material  directly  to  them  for  the 

178 


JOINERS'    RODS  179 

purpose  of  setting  it  out,  and  shaping  it.  These  drawings, 
in  the  case  of  carpentry  work  of  large  size,  are  usually  set 
out  with  chalk  upon  a  large  floor  or  platform  ;  in  the  case 
of  joinery  work,  in  pencil,  upon  planed  and  whitened  boards 
termed  "  rods,"  or  occasionally  upon  large  sheets  or  strips 
of  white  paper,  the  kind  used  by  paperhangers  for  lining 
ceilings.  Masons'  and  carvers'  work  is  usually  set  out  on 
sheets  of  brown  paper,  a  special  stiff  and  smooth-surfaced 
kind  ;  bricklayers'  work  either  on  "  centres  "  or  upon  large 
battened  "  boards,"  or  on  slabs  of  slate. 

Joiners'  Rods. — The  preparation  of  these  is  usually 
described  as  "  setting-out,"  but  the  term  should  not  be 
confused  with  the  operation  of  placing  shoulder  lines,  and 
marking  bevels,  scribes,  mortises,  tenons,  dovetails  and 
various  other  joints  upon  the  prepared  material,  which  is 
also  collectively  known  as  "  setting-out  "  in  the  workshop. 
With  this  latter  operation,  which  has  practically  nothing  to 
do  with  drawing  in  the  ordinary  sense  of  the  term,  this 
book  does  not  deal,  but  so  far  as  it  refers  to  joiners'  work 
the  subject  has  been  fully  described  in  the  author's  "  Modern 
Practical  Joinery." 

A  joiner's  "  rod  "  is  a  full-size  section  or  sections  of  the 
piece  of  work  to  be  executed,  and  is  intended  to  facilitate 
the  actual  setting-out  of  the  various  members  of  the  con- 
struction and  to  obtain  the  correct  quantities  of  the  material, 
also  to  be  a  convenient  record  for  future  reference  in  con- 
nection with  the  same,  or  other  work  upon  the  building. 
Obviously,  to  meet  these  requirements  the  drawing  should 
be  exact  as  to  shape  and  dimensions,  should  be  clear  and 
definite  as  to  the  intentions  of  the  person  setting  it  out,  and, 
saving  actual  blundering  or  ignorance  upon  the  part  of  the 
workman,  it  should  be  impossible  for  it  to  have  more  than 
one  reading. 

Foremen  and  "  setters-out  "  will,  of  course,  have  different 
opinions  as  to  what  is  necessary  to  place  upon  a  rod,  or 
what  to  omit,  and  the  instructions  given  herein,  though 
based  upon  the  author's  lengthy  experience  in  such  work, 


i8o  HOW    TO    SET    OUT 

can  only  be  taken  as  guides,  whose  course  it  may  be  neces- 
sary to  vary  with  circumstances.  In  the  author's  opinion 
the  simpler  a  rod  can  be  made  the  better  it  will  be  for  the 
workman — i.e.  no  superfluous  lines  should  be  employed, 
although  such  lines  represent  an  edge  or  a  member  in  the 
finished  work,  and  are  upon  the  architect's  drawing  ;  if 
they  are  not  actually  required  for  the  subsequent  setting- 
out  purposes  they  are  out  of  place  upon  the  rod,  and  likely 
to  lead  to  errors.  Inexperienced  setters-out  sometimes 
pride  themselves  upon  their  rods  being  "  pictures,"  and 
complacently  state  that  every  line  in  the  job  is  there. 
Probably  true,  to  the  discomfiture  of  the  workman  and  loss 
to  the  employer. 

Compare  the  two  sides  of  Fig.  3,  page  186,  and  consider 
which  is  the  easier  to  understand.  All  that  is  absolutely 
necessary  to  obtain  the  moulds  required  for  the  job  is  shown 
upon  the  right-hand  half,  and  the  left-hand  half,  though  a 
more  correct  drawing  in  elevation,  does  not  contain  all  that 
is  necessary,  and  it  contains  much  that  is  useless  and  liable 
to  mislead. 

It  often  requires  serious  consideration  as  to  the  best  way 
to  set  out  a  piece  of  work  on  the  rod ;  the  setter-out  must 
form  in  his  mind's  eye  the  completed  job  as  the  designer 
describes  it  in  the  drawings  and  specifications,  and  must 
decide  upon  the  main  principles  of  construction  ;  also,  if  it 
is  a  large  piece  of  work,  whether  it  can  be  fixed,  or  can  be 
conveyed  from  the  workshop  to  the  building,  in  one  piece. 
He,  of  course,  has  not  to  consider  the  minor  details  of  con- 
struction, the  "  putting  together  "  ;  this  is  a  matter  for  the 
workman,  but  careful  planning  is  often  necessary  to  ensure 
the  proper  fitting  and  arrangement  of  adjacent  parts,  in 
elaborate  finishings,  etc.,  that  have  to  be  set  out  in  sections 
or  portions  upon  several  rods.  Having  broadly  decided 
upon  the  construction,  the  next  essential  is  to  see  that  every 
piece  or  member  of  the  structure  has  its  length,  width  and 
thickness  shown,  and  that  parts  that  are  in  sections  are 
clearly  distinguished  from  those  shown  in  elevation,  upon 


WIDTH    OF    RODS  181 

the  same  drawing.  This  latter  is  usually  done  in  a  manner 
similar  to  ordinary  drawings,  by  pencilling  the  annual 
rings  in  wood,  in  a  conventional  manner,  and  indicating 
brick  or  stone  work  by  straight  lines  ruled  at  an  angle  of 
45°  on  the  parts  that  are  given  in  section.  Some  setters- 
out  prefer  to  use  coloured  pencils  to  indicate  these  materials : 
red  for  brickwork,  blue  for  stone,  yellow  for  iron,  etc.  In 
any  case  the  sectioning  should  be  merely  indicative,  and 
not  elaborate.  The  examples  in  this  book,  having  neces- 
sarily to  be  considerably  reduced,  appear  to  err  in  this 
direction,  consequent  upon  the  closing  in  of  the  lines  in 
the  reducing  process.  The  method  shown. in  Figs.  5  and 
6,  page  183,  of  short  straight  lines  around  the  outlines  of 
the  section,  is  a  very  good  and  clear  method,  and  allows 
of  writing  upon  the  member,  which  is  sometimes  advisable. 

No  graining  should  appear  upon  elevations,  as  a  stray  line 
may  be  mistaken  for  a  working  edge.  If  some  special  kind 
of  wood  is  required  in  a  certain  place,  such  as  a  mahogany 
strip  on  the  edge  of  a  deal  shelf,  it  is  better  either  to  write 
the  description  or  to  colour  the  portion  red,  or  such  other 
colour  as  will  best  indicate  the  material  to  be  used.  All 
chief  measurements,  such  as  clear  size  of  openings,  should  be 
figured  in  with  arrow-head  dimension  lines,  and,  when  a 
broken  section  is  given,  the  true  dimensions  should  always 
be  figured  across,  as  shown  in  Fig.  i,  page  186.  A  broken 
width  section  has  frequently  to  be  given,  as  in  the  example 
of  the  width  rod  just  quoted. 

Rods  are  seldom  used  wider  than  n  in.,  and  more 
usually  9  in.,  except  in  cases  where  the  work  cannot  pos- 
sibly be  draw  upon  such  widths.  Wide  boards  are  very 
inconvenient  to  handle,  occupy  a  great  deal  of  bench  space, 
and  thus  make  the  setting-out  costly.  It  is  generally  quite 
possible  to  show  all  three  dimensions  of  a  job  upon  a  narrow 
rod,  as  in  the  examples  (Figs,  i  and  3,  page  183,  and  Figs, 
i,  2,  4,  page  186).  Fig.  i  gives  the  width  of  a  door  and  the 
finishings,  but  not  the  width  of  the  linings  or  thickness  of 
the  wall  in  which  the  doorway  is  made.  This  is  shown 


1 82  DATUM    POINTS 

in  a  separate  drawing  made  upon  the  other  side  of  the  rod 
(see  Fig.  2)  ;  all  the  vertical  dimensions  are  shown  on  the 
"  height  rod,"  Fig.  4.  Thus  with  these  three  drawings 
the  joiner  can  obtain  all  the  dimensions  of  every  straight 
piece  in  the  job.  The  curved  portion  requiring  special  treat- 
ment will  be  referred  to  presently.  No  broken  lines  must 
be  made  in  the  length  of  a  section.  Obviously,  if  this  is  done, 
the  rod  is  useless  for  its  chief  purpose,  the  actual  laying 
down  of  the  stuff  upon  it,  and  the  transference  thereto  of 
the  shoulder  lines,  etc. 

The  breaks  in  the  examples  at  A9  Fig.  4,  and  B-B, 
(Figs.  2  and  3,  page  183),  are  introduced  to  avoid  making 
the  drawing  to  such  minute  scale  that  the  details  would  be 
indistinguishable,  but,  of  course,  in  actual  setting-out,  this 
would  not  need  consideration.  When  a  job  is  so  large  that 
more  than  one  rod  is  required  to  accommodate  its  length, 
as,  for  example,  a  dado  framing  for  a  30-ft.  corridor,  the 
adjacent  ends  should  be  squared,  and  correspondingly  num- 
bered or  lettered  within  circles,  and  the  exact  distance 
between  two  near  points  in  the  framing  should  be  figured 
in,  as  a  check,  in  case  the  rod  should  get  accidentally  cut 
short.  The  wall  or  other  "  fixed  point  "  should  always  be 
shown  on  the  width  rod,  and  the  floor  line  upon  the  height 
rod,  and  these  datum  points  are  the  ones  to  commence 
with. 

In  setting  out  linings  to  openings,  or  frames  to  fit  into 
them,  lay  down  the  dimensions  of  the  opening  first,  as 
ascertained  upon  the  building  or  from  other  data,  and  build 
the  framing,  as  it  were,  around  or  in  them  ;  by  this  method 
the  danger  of  making  a  fitting  either  too  large  or  too  small 
for  the  opening  will  be  avoided. 

Work  from  the  face,  or  best  side  of  the  job — -i.e.  from  the 
inside  of  a  window  or  the  more  important  side  of  a  door. 
Where  two  opposite  sides  of  a  job  are  alike,  as  the  two 
boxings  of  a  sash  frame,  do  not  set  out  each  independently, 
but  set  out  one  side  completely,  then  carefully  gauge  each 
line  from  the  face  edge  and  run  it  to  the  opposite  side  and 


JOINERS'    RODS 


183 


complete   the  section   therefrom,  which   ensures  accurate 
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A  Solid  Mullion  Venetian  Frame. — This  is  an 
example  of  how  the  work  may  be  set  out,  when  the  job 
is  wider  than  the  rod  to  be  used.  Fig.  i  is  the  height 


1 84  A    VENETIAN    FRAME 

rod,  and  it  contains  a  section  taken  through  one  of  the  side 
lights,  which  are  fixed,  the  central  pair  of  sashes  only  open- 
ing. This  is  indicated  by  the  grooves  for  the  cord  at  the  head. 
The  rod  is  9  in.  wide  and  the  frame  is  fixed  within  a  4!  in. 
reveal  in  a  13!  in.  wall,  which,  as  will  be  seen  by  the  en- 
larged detail,  Fig.  5,  leaves  gf  in.  to  be  covered  by  the 
frame  and  the  lining.  As  the  architrave  projects  beyond 
this,  it  is  obviously  impossible  to  put  it  all  in  on  9  inches. 
One  method  of  showing  the  parts  that  would  come  beyond 
the  edge  of  the  rod  is  given  at  A  and  B,  Fig.  I.  At  the  head, 
a  broken  section  is  shown  with  required  width  of  lining 
figured  in  ;  at  the  bottom  the  window  board  is  drawn  full 
width,  and  its  position  indicated  at  B'.  An  alternative 
method  of  showing  the  soffit  and  architrave  is  given  in  Fig.  4. 
Here  it  is  set  out  across  the  rod  at  one  end,  all  that  is  neces- 
sary for  the  workman  being  the  width  of  the  jamb  lining. 

To  avoid  showing  the  details  to  very  small  scale,  the 
width  rod,  Figs.  2  and  3,  is  drawn  as  if  in  two  parts,  the 
assumed  joint  being  at  C,  the  middle  of  the  central  light. 
Of  course,  this  is  merely  a  book  device  ;  the  actual  rod  would 
be  in  one  length.  The  usual  procedure  in  setting  out  this 
rod  would  be,  after  squaring  across  lines  to  represent  the 
bottom  side  of  the  sill  and  of  the  head,  to  draw  in  the  brick 
opening  as  shown  in  the  detail,  Fig.  5,  then  point  off,  suc- 
cessively, from  this,  the  outside  lining,  outside  sash,  parting 
bead,  inside  sash,  the  overlap  of  the  guard  bead,  and  finally, 
the  thickness  of  inside  lining,  which  completes  the  frame 
so  far  as  the  thickness  is  concerned.  Each  of  these  lines 
is  gauged  from  the  front  edge  of  the  rod  down  to  the  line 
of  sill.  Then  the  latter  is  drawn  in  by  aid  of  a  templet, 
or  to  the  required  section  according  to  the  details.  Next 
the  head  of  the  frame  is  completed  as  shown,  then  the  top 
rail  of  sash,  also  the  bottom  rail.  Then,  in  the  path  of  the 
top  sash,  mark  the  sight  line  of  the  bottom  rail  and  tick 
off  below,  the  thickness  that  the  meeting  rails  are  intended 
to  be,  in  this  case  if  in. ;  then,  if  half  of  the  distance  between 
the  lower  point  and  sight  line  of  top  rail  is  set  off  from  the 


CIRCULAR-HEADED    DOORS  185 

aforesaid  two  points  successively,  it  will  place  the  meeting 
rails  at  their  proper  thickness  exactly  midway  between 
the  sight  lines  of  the  top  and  bottom  rails.  The  drawing-in 
of  the  guard  beads  will  complete  the  height  rod. 

Make  a  note  on  the  rod  that  the  wide  bead  shown  at  the 
head  is  to  be  placed  in  the  outer  openings  only. 

A  Pair  of  Circular-headed  Doors  and  Finishings  are 
shown  on  page  186.  The  width  rod,  Fig.  I,  gives  the 
necessary  lines  for  setting-out  the  rails  of  the  doors,  width 
and  dishing  of  the  panels,  housing  or  grooving  in  the  soffit 
of  the  linings,  width  of  the  edging  E  (see  enlarged  details, 
Fig.  5),  also  width  of  the  head  of  the  grounds,  and  sight 
lines  for  moulds  and  sections  of  the  architrave.  The  rebate 
on  the  off  side  of  the  linings  is  perhaps  not  strictly  necessary, 
but  it  gives  the  joiner  a  better  idea  of  the  job  and  is  usually 
put  in.  The  width  across  the  linings  is  shown,  as  in  Fig.  2, 
either  upon  the  back  of  the  rod  or  farther  down  its  length 
upon  the  same  side  as  may  be  found  convenient.  The 
height  rod,  Fig.  4,  gives  the  heights  of  the  various  members 
between  floor  and  springing,  the  parts  above  the  springing 
(marked  SP)  are  given  merely  for  completeness,  or  to  make 
the  job  clear  to  the  workman,  as  he  does  not,  or  should  not, 
take  any  dimensions  from  it ;  all  of  these  must  be  taken 
from  the  elevation  rod,  Fig.  3,  and  the  necessary  data  for 
setting-out  the  height  rod  are  taken  from  Fig.  5.  For 
instance,  although  the  section  of  the  linings  and  archi- 
trave shown  on  Fig.  4  is  one  taken  at  the  centre  of  the  open- 
ing, that  of  the  door  is  taken  at  the  inside  edge  of  the  stile, 
which  is  the  nearest  point  to  the  centre  where  a  full  section 
of  the  rails  can  be  obtained. 

Elevation  Rod. — All  shaped  work  requires  an  "  eleva- 
tion rod  " — -i.e.  the  curves  must  be  set-out  full  size  to  obtain 
the  moulds  for  marking  out  the  stuff  from  which  the  several 
members  are  cut.  This  requirement  is  the  keynote  to  the 
setting-out.  Some  remarks  have  already  been  made  upon 
the  uselessness  of  embellishing  the  rod  with  lines  that  are 
not  necessary — i.e.  not  required  for  the  actual  setting-out  of 


HOW    TO    SET-OUT  187 

the  work.  To  make  this  quite  clear  :  the  architrave  mould- 
ing shown  in  section  at  top  of  Fig.  4,  and  in  detail  at  Fig.  5, 
contains,  in  its  finished  state,  eleven  arrises,  which  require 
eleven  lines  on  the  rod  to  indicate  them.  Now  all  that  is 
required  to  draw  the  moulds  are  four  lines,  the  inner  and 
outer  edges  of  each  piece.  When  the  stuff  is  cut  to  this 
shape,  the  machinist  will  automatically  produce  all  the 
others  with  correctness,  by  working  the  face  edge  against 
the  "  spindle,"  therefore  these  extra  lines  are  not  only 
useless  on  the  rod,  they  are  confusing,  also  when  the  work- 
man is  trying  the  moulds  on,  he  requires  to  keep  following 
the  path  of  such  lines  around,  to  make  sure  he  is  dealing 
with  the  right  one. 

To  set  the  Rod  out. — Draw  the  springing  line  and  a 
centre  line  at  right  angles  to  it,  squaring  from  lower  edge  of 
board.  Draw  in  the  frieze  rails  and  stiles,  also  section  of 
the  architrave  on  one  side  exactly  as  they  occur  on  the 
width  rod.  Strike  the  door  head  with  a  beam  compass, 
also  the  curved  panels  ;  mark  in  the  radial  joint  line. 
Next  consider  what  is  required  in  the  way  of  moulds.  There 
will  be,  in  the  present  case,  one  each  for  back  architrave 
M ;  bed  mould  B  ;  ground  G  ;  solid  rebate  E  ;  soffit  stile  or 
head  L  ;  and  panel  of  same,  also  one  for  panel  of  door ;  this 
latter  is  shown  in  the  second  line  on  right  side  of  door.  The 
various  moulds  are  indicated  by  the  above  letters  in  the 
example,  and  the  same  letters  are  used  on  the  enlarged 
section  for  reference.  To  avoid  confusion,  the  soffit  is 
shown  separately  in  Fig.  6,  but  as  the  Hnes  would  not  be  so 
close  together  when  set  out  full  size,  this  could  be  super- 
posed on  the  same  rod. 

It  is  considered  somewhat  infra  dig.  by  most  joiners  to 
have  the  various  constructive  joints  shown  on  the  rod, 
as  they  are  presumed  to  know  the  rudiments  of  their  trade, 
but  as  the  correct  size  and  disposition  of  tenons,  etc.,  is  of 
more  importance  in  circular  work  than  in  square,  it  is  very 
usual  to  set  these  out  on  the  rod.  The  tenon  on  the  left  of 
Fig.  3  is  the  way  not  to  do  it ;  that  on  the  right  the  correct  way. 


188  SETTING-OUT    FOR    BRICKLAYERS 

In  the  first  case,  probably  half  the  tenon  would  break 
off  in  the  wedging  up,  through  being  cut  across  the  grain. 
The  joints  in  the  door  head  would  be  grooved  and  cross- 
tongued  and  handrail-bolted ;  those  of  the  architrave, 
dovetail-keyed  ;  the  grounds,  half-lapped  and  screwed  ; 
and  those  between  soffit  and  jambs,  do  welled. 

Bricklayers'  Setting-out.— Circle-on-circle  work,  Figs, 
i  and  2,  page  189,  show  the  half  elevation  and  half 
plan  of  a  semicircular  arch  in  a  circular  wall,  the  jambs, 
reveals  and  soffits  of  the  opening  being  perpendicular  to 
the  chord  line  of  the  arc,  or,  as  it  is  more  usually  described 
in  the  trade,  an  opening  with  parallel  jambs  and  soffit  level 
at  the  crown. 

These  arches  are  invariably  made  in  gauged  or  cut  work, 
and  the  usual  practice  is  for  the  carpenter  to  make  a  true 
"  centre  "  to  fit  the  required  opening  exactly  in  both  plan 
and  elevation,  and  the  bricklayer,  having  first  made  an 
elevation  on  his  bench  board  full  size,  applies  the  centre  to 
the  drawing  and  marks  the  intrados  spacing  of  the  arch  on 
each  face  in  turn,  and  then  joins  up  the  points  across  the 
soffit  with  a  straight  edge,  thus  obtaining  the  shape  of  each 
brick  on  the  soffit.  This  method  has  its  drawbacks,  as 
each  brick  must  be  scribed  to  the  faces  of  the  "  centre," 
and  it  is  necessary  for  the  carpenter  to  make  a  "  centre  " 
with  compound  curves,  which  is  much  more  expensive 
than  an  ordinary  barrel  centre  with  which  the  job  could  be 
done  equally  well  by  the  method  of  setting-out  now  to  be 
described. 

To  set  out  the  Elevation. — Draw  the  springing  line 
parallel  to  the  edge  of  setting-out  board,  and  far  enough 
upwards  to  get  the  plan  underneath  as  shown  in  the  ex- 
ample. It  is  usual  to  strike  the  entire  arch,  but  one-half 
is  really  sufficient.  Draw  a  centre  line  with  the  square, 
and  at  the  intersection  as  centre  and  the  "  trammel  rod  " 
set  to  the  required  radius,  strike  the  intrados  and  extrados 
of  the  arch,  set  out  the  springers  and  the  key  brick,  the  first 
on  the  springing  line  and  the  second  equally  on  each  side 


190  DETAILS    OF    ROD 

of  centre  line,  then  space  out  the  extrados  equally,  with  the 
compasses  set  to  the  thickness  of  a  brick,  and,  if  the  arc 
will  not  divide  equally  with  this,  reduce  the  space  until  an 
equal  division  can  be  obtained,  then  draw  the  joints  radiating 
from  the  centre  to  the  division  points.  This  will  give  size  of 
templet  for  the  faces,  to  which  the  cutting  box  should  be 
made. 

Next,  strike  out  the  plan  on  the  same  centre  line,  and 
square  the  reveals  and  jambs  from  edge  of  board.  Draw  in 
the  plans  of  the  bed  joints  by  moving  the  square  around 
the  soffit  successively,  as  shown  by  the  numbers  on  Fig.  I 
and  indicated  by  dotted  projector  at  joint  No.  13.  This 
gives  the  soffit  joints  or  end  shape  of  the  bricks  in  plan  only, 
but  not  their  real  size ;  to  obtain  this  a  stretch-out  of  the 
soffit  as  shown  in  Fig.  3  is  required.  To  obtain  this,  make  the 
line  a'~a  equal  in  length  to  the  curve  line  S-C,  Fig.  i,  and 
this  can  be  done  accurately  enough  by  setting  the  com- 
passes to  the  thickness  of  a  brick  on  the  soffit  as  seen  in  the 
elevation,  and  stepping  it  along  the  line  the  number  of 
times  there  are  bricks  in  the  arch.  (Only  one-half  is  shown, 
and  this  is  usually  sufficient.)  Next  draw  perpendiculars 
from  the  division  points  of  indefinite  length,  with  the  square. 
Then  draw  a  line  tangent  to  the  plan  curve — -i.e.  parallel 
with  the  springing  line — -and  carry  the  joints  across  to  it, 
as  shown  by  dotted  projectors.  Number  each  set  as  shown, 
then,  measuring  across  each  joint  with  the  compasses  from 
the  tangent  line,  transfer  the  lengths  to  the  stretch-out  line 
upon  the  corresponding  number  thereon,  and  so  obtain  a 
series  of  points  through  which  the  curves  can  be  drawn, 
by  bending  a  lath  to  fit  them.  Now  we  have  the  soffit  as 
it  would  appear  if  stretched  out  flat,  but  as  the  arch  is 
curved,  this  does  not  really  give  the  accurate  angles  of  each 
individual  brick,  and  we  must  bend  this  stretch-out  over 
the  centre  before  we  can  get  the  true  shapes.  The  best 
way  to  do  this  is  to  trace  off  the  stretch-out  on  a  strip  of 
tracing  linen,  then  to  fasten  this  upon  the  "  centre  "  with 
tacks  keeping  the  crown  at  its  proper  projection  beyond 


CIRCLE-ON-CIRCLE    WORK  191 

the  springings  as  shown  in  Fig.  2,  the  bevels  can  then  be 
taken  and  the  cutting  proceeded  with. 

A  Circle-on-Circle  Opening  with  splayed  jambs  and 
soffit  is  shown  in  Figs.  4,  5  and  6.  Obtaining  the  shape  of 
the  bricks  for  this  arch  is  a  somewhat  more  complicated 
process  than  the  last  case,  which  was,  in  effect,  the  deter- 
mination of  the  penetrating  section  of  two  right  cylinders, 
whilst  this  one  is  the  penetration  of  a  right  cylinder  by  a 
semi-cone,  and  the  method  of  obtaining  the  shape  of  the 
soffit  is  based  on  the  process  of  obtaining  the  covering  of 
a  cone  as  described  on  page  159.  Much  of  the  previous 
instruction  will  apply  to  this  case  and  it  will  only  be 
necessary  to  recapitulate. 

Having  struck  the  arch,  draw  the  bed  joints  to  the  centre, 
and  project  the  soffit  ends  into  the  face  of  the  plan,  as  shown 
by  the  dotted  projectors  5  and  70.  Produce  the  side  of  the 
reveal  to  the  centre  of  the  plan  curve  C,  and  draw  the  plans 
of  the  joints  all  to  the  same  centre.  These  lines  have  not 
been  produced  in  the  example,  to  avoid  confusion. 

To  draw  the  Section,  Fig.  6,  project  the  crown  and 
springing  of  the  arch  across,  as  shown,  to  the  face  of  the 
wall ;  continue  the  face  line  down  to  the  springing  to  pro- 
vide a  plane  to  measure  from.  Project  horizontal  lines  from 
the  intersections  of  each  joint  with  the  back  and  front  edges 
of  the  arch.  One  or  two  only  of  these  are  shown,  and  one  will 
be  traced  throughout  as  a  guide  to  the  rest.  Take  the  top 
bed  joint  of  the  seventh  brick  (point  7  in  Fig.  4),  project  a 
horizontal  across  to  X,  also  drop  a  projector  from  same 
point  into  the  plan  at  ja ;  carry  this  to  the  centre  line  in 
point  yb  by  a  perpendicular  therefrom.  Transfer  the  dis- 
tance of  yb  from  C'  to  the  line  S,  Fig.  6,  which  gives  point 
7" ;  erect  a  perpendicular  to  meet  the  horizontal  projector 
j-x  in  point  7°,  which  is  a  point  in  the  curve  to  be  drawn. 
Follow  out  each  joint  in  like  manner  on  each  edge  of  the 
arch,  and  draw  the  curve  through  the  points  so  found. 

To  obtain  Soffit  Mould. — This  has  been  laid  out  over 
the  plan,  and  the  mould  is  hatched  to  make  it  distinctive. 


192  OCTAGONAL    CHIMNEY 

Draw  the  tangent  line  C-D,  and  produce  the  splayed  reveal 
to  meet  it.  With  C'  as  centre  and  C'-D  as  radius,  describe 
an  arc ;  this  is  the  base  of  the  semi-cone  C-C'-D  laid  down. 
With  the  apex  C  as  centre  and  side  C-D  as  radius,  describe 
the  arc  D-C".  Next,  produce  the  joint  lines  in  the  plan 
to  meet  the  line  C'-D,  and  thence  erect  perpendiculars  to 
cut  the  curve  in  points  i  to  14.  Transfer  these  divisions  to 
the  curve  line  D-C",  numbering  them  to  correspond.  Draw 
lines  from  these  points  to  C,  which  will  be  the  direction 
of  the  joint  lines  upon  the  soffit  or  "  centre"  developed. 
To  obtain  the  faces  of  the  arch,  mark  off  a  distance  on  each 
of  these  lines  from  D-C"  equal  to  the  distance  of  the  plan 
of  the  arch  from  the  tangent  line  C'-D,  at  the  corresponding 
joint,  and  thus  obtain  points  through  which  the  curves  can 
be  drawn.  Trace  these  on  linen  and  fix  to  the  conical 
"  centre,"  when  the  true  shape  of  each  brick  will  be  visible. 
The  back  arch  is  usually  "  axed  "  to  shape  on  the  centre, 
as  it  is  either  covered  by  plaster  or  wood  linings. 

To  set  out  an  Octagonal  Chimney  Stack  (see  page  189). 
— Figs.  7  and  8  are  the  elevation  and  half  plans  at  cap  and 
neck  respectively  of  a  group  of  four  octagonal  chimneys  rising 
from  a  square  base.  The  detail,  Fig.  9,  shows  the  method 
of  setting-out  the  stack  full  size  to  obtain  shapes  of  the 
bricks  and  the  bonding.  The  back  pair  shows  the  course 
above  or  below  the  front  pair,  if  moved  forward  horizontally, 
and  the  dotted  lines  indicate  the  joints  below.  Only  two 
templets  are  required  for  the  shafts  as  shown  in  Fig.  n, 
Nos.  i  and  2,  and  two  for  the  cap,  Nos.  3  and  4. 

Two  Methods  of  setting-out  Octagons  are  shown  in 
Fig.  10  :  that  on  the  left  is  more  suitable  for  draughtsmen's 
work  with  instruments,  that  on  the  right  for  workshop  use, 
as  this  can  be  set  out  with  a  square  and  straight  edge. 

First  Method. — Let  the  width  of  the  required  octagon  be 
given  as  a-b.  Draw  a  square  to  the  given  dimension  as 
a—b-c-d,  bisect  one  side  and  draw  a  centre  line,  bisect  this 
line  and  find  the  centre  e.  With  a-e  as  radius  and  a,  b,  c,  d 
as  centres,  describe  arcs  cutting  the  sides  of  the  square 


SETTING-OUT    OCTAGONS  193 

at  i,  2,  3,  4,  etc.  Join  up  these  points  and  the  octagon  will 
be  described. 

Second  Method. — Let  the  width  be  known.  Construct 
a  square  to  the  given  width  and  draw  two  diagonals.  Mark 
off  from  centre  C,  along  each  diagonal  half,  the  width  of  the 
required  octagon.  Through  these  points  draw  lines  parallel 
to  the  diagonals,  so  constructing  a  second  square  over- 
lapping the  first,  which  will  produce  an  octagon  as  shown. 

The  bevels  shown  on  the  left  octagon  are  those  used  for 
marking  the  templets,  and  are  placed  there  for  convenience ; 
they  can  easily  be  identified  by  the  letters.  A  is  the  bevel 
for  the  cap  joint  No.  4,  B  the  bevel  for  the  shaft  joints 
Nos.  i  and  2  (see  Fig.  9  for  further  identification). 


INDEX 


ALPHABETS,  42 

Angle  braces,  cuts  in,  145 

Angles,  brace  in,  145  ;  com- 
pound, 142  ;  simple,  142  ; 
to  measure,  15 

Apron  piece,  76 

Arch,  basket-handle,  169 ; 
bell,  172  ;  camber,  167  ; 
carpenter's,  169  ;  circle- 
on-circle,  78,  188,  191  ; 
cyma  reversa,  172  ;  drop, 
170  ;  discharging,  66, 165, 
166  ;  elliptic,  167  ;  equi- 
lateral, 168  ;  flat,  167  ; 
false  ellipse,  168,  179  ; 
four-centred,  168,  170 ; 
gauged,  66,  164 ;  horse- 
shoe, 169 ;  lancet,  168, 
170 ;  masonry,  165  ; 
Moorish,  169  ;  ogee,  169, 
172  ;  pointed,  165,  171  ; 
round,  165,  169  ;  stilted, 
169 ;  squinch,  169  ; 
Tudor,  168,  170  ;  wave, 
172 

Architectural  curves,  12,  28 

Architrave,  65,  68,  77,  149, 
183,  186 

B 

BACKINGS,  96 
Bagatelle  hinge,  136 
Basket-handle  arch,  169 
Bell  arch,  172 


Bevels,  angle  braces  on,  147  ; 
brick  arches  in,  191  ;  how 
to  find,  141,  147  ;  oblique 
planes,  144,  146 ;  octa- 
gonal chimney,  193  ; 
splayed  linings  in,  77,  148 

Billiard-room,  lantern  for,  76 

Bow  compasses,  14 

Box  cleats,  112 

Bracket,  68,  87 

Breastsummer,  65 

Brick  arches,  164,  165,  167, 
168 

Bricklayers,  ellipse,  154 ; 
setting-out,  188,  193 

Bridging  joist,  64 

Builder's  gantry,  94 

Butt  hinges,  134,  136,  138 

Button,  70,  96 


CABINET   screwdriver,    129, 

131 

Carpentry  arches,  169,  171 

Cartridge  paper,  16 

Carved  and  moulded  window 
head,  133 

Chain-line,  use  of,   31 

Circles,  describing,  30 ; 
isometric  projection  of,  96 

Circle-on-circle  doors,  77  ; 
obtaining  moulds  for,  79, 
80,  8 1  ;  methods  of  pro- 
jection, 78 

194 


INDEX 


195 


Circle-on-circle  opening,  191 

Circular-headed  door,  185 

Cock  bead,  67 

Compasses,  beam,  14  ;  bow, 
14  ;  choice  of,  13  ;  how  to 
use,  30  ;  lengthening  bar 
for,  13  ;  sizes  of,  13 

Complex  curves  in  isometric, 

99 
Cone,  covering  of,  79,  159  ; 

definition  of,  155  ;  frustum 
of,  159  ;  penetration  of 
cylinder  and,  191  ;  pro- 
jection of,  156  ;  properties 
of,  155  ;  ungula  of,  156  ; 
visual  rays,  114 

Conic  sections,  155, 156 

Corbel,  57 

Counter,  details  of,  70  ;  flap 
hinge,  138  ;  view  of,  95 

Counter-lath,  105 

Covering  of,  cones,  79,  159  ; 
domes,  160, 162  ;  roofs,  55 

Cross  garnet,  139 

Cube,  projection  of,  83,  101 

Cupboard,  50,  89 

Curb,  73,  74,  76 

Curved  lines,  how  to  draw, 
128  ;  measuring,  30 

Cylinder  in  isometric,  97 

D 

DAMP  stretching,  24 
Dimensions,   lines,   32  ;     to 

lay  off,  29 
Discharging  arch,   66,   165, 

166 

Dividers,  13 
Dogs,  use  of,  94 
Domes,  159,  164  ;   covering 

of,  159,  160,  162 


Doors,    circle-on-circle,   73  ; 

circular  -  headed,        185  ; 

diminished      stile,      62 ; 

framed,  ledged  and  braced, 

60,  61  ;   how  to  draw,  61, 

63  ;     how   specified,    61  ; 

panelled,  61 

Draper's  counter,  69,  94 
Draughtsman's  cardinal  rule, 

5  ;    faults,  27,  53  ;    lines, 

31,   34  ;     sectioning,   34  ; 

signs,  31 

Drawer  details,  70 
Drawing    accessories,     16 ; 

boards,  8,  9  ;   curves,  27, 

128  ;  frame,  65  ;  freehand, 

127  ;  heading,  size  of,  38  ; 

how  to  commence,  28,  29  ; 

ink,   19  ;  paper,   16,   17  ; 

pencils,  17,  18  ;  pens,  44 ; 

pins,  18  ;    scales  for,  21  ; 

squares,  10,  25 
Drawing  board,  attachments 

to,  9  ;    how  to  make,  9  ; 

materials,    8  ;     sizes,    8  ; 

varieties  of,  8,  9 
Drawing   circles,    hints   on, 

30,  31 
Dwarf  cupboard,  50,  89 


ELLIPSE,  definition  of,  150  ; 
false,  154,  168  ;  isometric 
in,  98 ;  methods  of  drawing, 
150,  151,  153,  154,  157; 
properties  of,  150,  155  ; 
trammelling,  151,  153 

Elliptic  arch,  155,  167 ; 
dome,  164  ;  head  to  frame, 
78  ;  mould,  80  ;  section 
of  cone,  157  ;  section  of 
cylinder,  151 


196 


INDEX 


Enlarging     drawings,     133, 

135 

Entrance  door  and  frame,  77 
Espagnolette  bolt,  68 
Examinations,  drawing  at, 

29 
Examination  question,  76 


FACE  mould,  80 

False  ellipse,  154,  168 

False  lines,  how  treated,  32 

Fan,  93 

Fanlight,  67 

Fender,  93 

Field  gate,  53,  54 

Finding  marks,  24 

Finial,  joints  in,  72,  74 

Finishings,    185 

Fixing  drawing  paper,  24 

Floors,  how  to  draw,  63  ; 
plan  of,  64  ;  single,  a,  63  ; 
spring,  140 

Formation  of  letters,  44 

Forms,  no  ;  for  beams,  how 
made,  in 

Footings,  91 

Freehand  drawing  or  sketch- 
ing, 127-140 

Freehand  copying  mould- 
ings, 130  ;  curves,  how  to 
draw,  128 ;  cylinder  in, 
131  ;  definition  of,  6, 127  ; 
use  of  the  pencil  in,  128  ; 
use  of  squared  paper  in, 
132 

French  casements,  67,  69, 
148 

French  curves,  12,  28 

Frog  in  bricks,  3 


Frogs,  how  laid,  92 
Frustum,  156 


GAUGED_arch,  66,  164,  188 
Gate,  54";  hinges,  53,  139 
Geometry,  examples  in,  141- 

177  ;  practical,  definition 

of,  6 

Gibs  and  cottars,  55 
Gothic  dome,  163 
Graining,  use  of,  33 
Grounds,  66,  68, 106, 183 


H 
HATCHINGS,    standard    list, 

33,  34 

Helical  curve,  175 

Helical  hinge,  138 

Helix,  definition  of,  172  ; 
to  draw,  174 ;  develop- 
ment of,  175 

Herring-bone  strutting,  64 

Hexagon,  103 

Hexagonal  prism,  103 

Hinges,  134-139 

Hints  on  drawing,  24-34 

Hook-and-eye  hinge,  139  ; 
joint,  68 

How  to  set-out  a  rod,  187 

Hyperbola,  158 


INK,  Indian,  19  ;   lettering, 

45  ;  waterproof,  19 
Inking-in,  27  ;  curves,  28 
Instruments,  description  of, 
12 


INDEX 


197 


Isometric  projection,  82-0,9 ; 
advantages  of,  82  ;  basis 
of,  82  ;  definition,  3  ; 
derivation  of  term,  82 ; 
Parish's  method,  85  ; 
planes,  88 ;  scale,  84 ; 
theory  of,  3,  82,  85 

Isometric  projections,  brick 
quoin,  91  ;  builder's 
gantry,  93  ;  cube  of  a,  86  ; 
dwarf  cupboard,  50;  frame, 
88  ;  nest  of  shelves,  88  ; 
octagonal  prism,  88  ;  octa- 
gonal pyramid,  90  ;  wash- 
ing tray,  90 


JAMB,  59, 190  ;  lining  in,  68, 
105  ;  splayed,  148 

Joiner's  rods,  179,  183,  186 

Joining  circular  to  straight 
lines,  28 

Joints,  compasses  in,  13  ; 
covering,  67  ;  cupboard, 
89 ;  doors  in,  59,  62  ; 
drawing  boards  in,  8 ; 
finials  at,  72  ;  in  floors, 
64 ;  in  gate,  53  ;  hook, 
68  ;  in  roofs,  56,  77  ; 
windows,  67 

Joists,  sizes,  63 

K 

KING  closer,  66 
King  post  truss,  55 


LAMINATED  rib,  57,  58 
Length  of   a   semicircle,  to 
obtain,  30 


Lettering,  balance  in,  41  ; 
details  of,  36,  43,  44; 
faults  in,  36  ;  importance 
of,  35  ;  objects  of,  35  ; 
proportions,  41  ;  slope  in, 
41  ;  spacing,  42  ;  styles, 
35  ;  tools  in,  44  ;  styles 
of,  35 

Lettering  drawings,  35-45 

Lines,  various  kinds  used  by 
draughtsmen,  31-34 

Lining  piece,  70 

Lining-in,  27 

Linings,  68  ;  splayed,  148  ; 
rod  for,  186  ;  width  of, 


85  ; 


130 


Lower  case  letters,  38 


M 

MASON'S  arch,  167 
Masonry  details,    129,   132- 

133,  135 
Measuring       angles, 

curved  lines,  30 
Mortise  lock,  62 
Mouldings,    to    copy, 

(see  Doors) 
Moulds  for  bricklayers,  191  ; 

circular  frame,   79  ;   door 

frame,  80  ;    hips,  73 
Mullion,  68,  75 
Munting,  59,  62 


N 

NAKED  floor,  64 
Normals,  154 
Numerals,  40 


I98 


INDEX 


O 


OBLIQUE  cones,  155,  156 

Oblique  planes,  bevels  in, 
141 

Oblique  projection,  100-113 

Oblique  projection  dimi- 
nished, 105  ;  half  scale, 
102,  103  ;  theory  of,  102 

Oblique  projection,  varieties 
of,  100 

Oblique  scale,  106 

Octagon  chimneys,  192 ; 
roofs,  72  ;  setting-out  an, 
192-193 

Octagonal  roof,  71,  72  ; 
prism,  88  ;  pyramid,  87 

Octagons,  87,  192 

Ogee  arch,  171  ;  mouldings, 
59  ;  roof,  72 

Optical  corrections  in  letter- 
ing. 44 

Ordinates,  definition  of,  10 ; 
of  ellipse,  151,  157 ;  of 
parabola,  158 

Orthographic  projection,  46- 
81 

Orthographic  projection, 
meaning  of  term,  48 ; 
principles  of,  2 


PARABOLA,  158 
Parliament  hinge,   138 
Parallel  lines,  drawing,  25  ; 

projection,  3  ;    rule,  14 
Pedestal,     a     stone,     120 ; 

table,    124 
Pencils,     degrees    in,     17 ; 

compass,      18  ;     holding, 

129 ;  sharpening,  26 


Pentagons,   107,    108 
Perpendicular,  definition  of, 

25 

Perpendicular  projection,  2 

Perspective  or  radical  pro- 
jection, 114-126 

Perspective,  a  large  chest 
in,  122  ;  definition  of,  5 
(see  also  p.  115) ;  pedes- 
tal table,  124 ;  picture 
plane,  116 ;  rectangular 
frame  in,  119 ;  stone 
pedestal  in,  120  ;  symbols 
used  in,  114  ;  theory  of, 
118  ;  vanishing  points  in, 
119 

Pew  hinge,  138 

Pin  lifter,  19 

Planes,  auxiliary,  49 ;  co- 
ordinate, 49  ;  ground,  116  ; 
horizontal,  116  ;  isometric 
oblique,  141 ;  picture,  116; 
section  of,  158 ;  spiral,  176 ; 
vanishing,  176 ;  vertical, 

49 

Planes,  block,  51 ;  chest,  123 ; 
counter,  70  ;  cupboard, 
51  ;  definition  of,  2  ; 
doors,  59,  62,  76*1 ;  frame, 
117;  floor,  64;  gate, 
53 ;  grating,  107 ;  how 
obtained,  49  ;  lantern, 
75  ;  roof,  72  ;  window,  66 

Platform,  93 

Plinth  block,  65,  68,  77,  149 

Pocket  piece,  66 

Pole  plate,  55,  57 

Practical  geometry,  141- 
177 

Prism,  hexagonal,  101  ; 
octagonal,  87 ;  pentagonal 
107 


INDEX 


199 


Projection,  comparative 
types  of,  3  ;  isometric,  3, 
82  ;  oblique.  3,  100  ; 
orthographic,  2,  46 ; 
perpendicular,  2 ;  perspec- 
tive, 5, 114 ;  principles  of, 
3  ;  radial,  5,  114 

Pulley  stile,  68 

Purlin,  55,  73,  163 ;  obtain- 
ing cuts  in,  145 

Pyramid,  octagonal,  90  ; 
pentagonal,  107 

Q 

QUEEN  post  truss,  75,  76 
Quoin,  92 

R 

RACKING  back,  92 

Radial  projection,  5,  114 

Reinforced  concrete  work, 
no 

Rib  roof,  57 

Ribs,  72,  161 

Ridge  tiles,  55 

Rods,  for  bricklayers,  179  ; 
189  ;  for  carpenters,  179  ; 
elevation,  185  ;  for  joiners, 
179,  183,  186  ;  to  set-out, 
187  ;  width  of,  181 

Roofs,  collar  beam,  56  ; 
collar  bolt  and  tie,  56  ; 
couple,  54  I  couple  close, 
56  ;  drawing,  56,  60  ;  Emy, 
58  ;  king-post,  56  ;  lamin- 
ated rib,  57,  58  ;  lantern 
in,  75  ;  octagonal,  71  ; 
ogee  pavilion,  72 ;  pavilion, 
72  ;  queen  post,  75  ;  types 

of,  55 
Root  lines  in  isometric,  86 


Rubber,  18 

Ruling  pen,  1 1  ;   description 

of,  14  ;  to  hold,  27 
Runners,    70 


SCALES — architectural,    21 
construction        of,       21 
diagonal,   22 ;   engineers' 
22 ;        isometric,        83 
materials,     19  ;     oblique, 
106  ;  representative  frac- 
tion in,  20  ;  squared  paper 
as,  134 

Screw  wrench,  132 

Scroll,  176,  177 

Section,  meaning  of,  3 

Serif,  38 

Setter-out,  a,  6 

Setting-out,  denned,  179 

Setting-out ;       bricklayer's, 
188  ;   methods  of,    180 

Sharpening  pencils,  26 

Shop  fittings,  69,  71 

Shuttering,  construction  of, 

IIO-III 

Skewback,   186 

Skylight,    76 

Soffit,   arch,   78,  188,   191 
bricks,    shape    of,     188 
development      of,      149 
linings,  148,  185  ;  moulds, 
79,  191  ;  splayed,  191 

Solid  frames,  59,  63,  67,  68, 
77,  148,  170,  183 

Spacing  in  lettering,  42 

Spherical  domes,  161 

Spiral,  definition  of,  176 ;  to 
draw  a,  176 

Splayed  linings,  bevels  for, 
148  ;  reveals,  77,  149,  191 


200 


INDEX 


Spring  bow,  14 

Spring  hinge,  140 

Squares — how  to  make,  10  ; 
materials,  10  ;  set,  sizes  of, 
10 ;  T,  10  ;  use  of,  25, 
45  ;  using,  25,  50,  86, 
varieties,  10 

Squared  paper,  how  to  use, 
132  ;  as  a  scale,  134 

Strap  hinge,  59,   137,    138, 

139 
Stone  baluster,  129, 131 


TECHNICAL    drawing,    vari- 
ous kinds  of,  17 
Templets,  166,  167,  190 
Tie  beam,  55,  75 
Tools  used  in  lettering,  44, 

45 

Tracing  paper,  19 
Transom,  67,  68,  69 
Trestle  hinge,   138 
Trimmers,  63 
Trussed      partition,      104 ; 

doorway  in,  105 
Trusses,  55,  57 
Tusk  tenon,  64 
Types  in  lettering,  38,  42  ; 

alphabets,  42 ;  black  letter, 

39  ;  block,  37,  39  ;  cursive, 

40;      Egyptian,     39; 

italics,    39  ;    roman,    38  ; 

sanserif,   39  ;    stone,    39 ; 

stump,  40 


U 

UNGULA,  155 

Uniformity  in  lettering,  40, 

43 
Upper  case  letters,  38 

V 

VENETIAN  frame,  183 
Ventilator,  107 
Voussoirs;  165  ;  templets  for, 
167 

W 

WALL  plates,  55,  57 

Wall  post,  57 

Water  bar,  position  of,  67 

Water-groove,  68 

Weather  board,  67 

Weep  pipe,  69,  76 

Window  board,  66 

Windows,  65,  66,  67,  68 ; 
back,  65,  66 ;  bay,  64  ; 
casement,  67  ;  head  stone, 
133  ;  how  to  draw,  65  ; 
nosing,  68  ;  sash  frames, 
65  ;  Venetian,  183  ;  ven- 
tilating piece,  65 

Window  head  in  stone,  132 

Wood  grating,  107 

Working  drawings,  defini- 
tion, 6 ;  examples  of,  51, 
59,  68,  70,  75 

Workshop  drawings,  178- 
193  ;  definition  of,  7, 
178  ;  examples  of,  51, 183, 
186,  189 

Wreathed  handrail,  175 


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